3x - 2 (x + 3) = 4x - 7

Answers

Answer 1

The answer: " x = ⅓ " .
____________________________________________________
Given: " 3x − 2 (x + 3) = 4x − 7 " ; Solve for "x" ;
____________________________________________________

Start with the following term on the "left-hand side" of the equation:

" - 2 (x + 3) " ;
____________________________________________________
Note the "distributive property of multiplication" :
____________________________________________________
a(b + c) = ab + ac ;

a(b − c) = ab − ac ;
____________________________________________________
As such,

" -2 (x + 3) = -2(x) + -2(3) = -2x + (-6) = -2x − 6 ;
____________________________________________________
So, we can rewrite our equation:
____________________________________________________
" 3x − 2 (x + 3) = 4x − 7 " ; substituting: " -2x − 6" (for " −2 (x + 3)" ; as follows:
____________________________________________________

3x − 2x − 6 = 4x − 7 ;
___________________________________________________
On the left-hand side off the equation;
________________________________
We can combine the "like terms" ; as follows:

3x − 2x = 1x = x ; and rewrite the equation:
__________________________________
x − 6 = 4x − 7 ;

____________________________________
We can subtract "4x" from each side of the equation; and add "6" to each side of the equation:
____________________________________
x − 6 − 4x + 6 = 4x − 7 − 4x + 6 ;

to get: -3x = -1 ;
____________________________________
Now, we divide EACH SIDE of the equation by "-3" ; to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;
____________________________________
-3x / 3 = -1/-3 ;
____________________________________
to get: x = ⅓ .
_____________________________________
→ Now, let us check our answer by plugging in "⅓" for all values of "x" in the ORIGINAL GIVEN EQUATION; to see if the equation holds true:
_____________________________________________________
  →   3x − 2 (x + 3) = 4x − 7 ;

  → [3 * (⅓) ] − 2 [ (⅓) + 3) = ? 4(⅓) − 7 ?? ;

  → (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;

  → (1) − 2(3 ⅓) =? (⁴/₃) − 7 ?? ;

  → (³/₃) − 2(¹⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;

→ (³/₃) − (²⁰/₃) =? (⁴/₃) − (²¹/₃) ?? ;

→ ⁽³ ⁻²⁰⁾/₃) =? ⁽⁴⁻²¹⁾/₃) ??

→   ⁻¹⁷/₃ = ? ⁻¹⁷/₃ ?? Yes! Our answer "makes sense"!
_____________________________________________________

Related Questions

4 3/2
-
3 1/4
________

Answers

4 3/2-3 1/4
11/2-13/4
(22-13)/4
9/4
2 1/4

3 1
4 --- - 3 ---
2 4

11 13
--- - ---- Common denominator is 4
2 4 Multiply first fraction by 2
(2) (1)

22 13
--- - ---
4 4

9
---
4

1
2 ---
4

What is 485 times 34

Answers

the answer is 16,490

16,490 is the answer to your question.

the difference of a positive integer and its inverse is 15/4. find the integer

Answers

If the integer is x, and the inverse is 1/x, we have x-1/x=15/4 (since difference is subtraction). Multiplying both sides by x, we get x²-1=15x/4. Next, we can subtract 15x/4=3.75x from both sides to get x²-3.75x-1=0. Using the quadratic formula, we get [tex]x= \frac{3.75+- \sqrt{(-3.75)^2-(4*-1*1)} }{2} = \frac{3.75+- \sqrt{14.0625+4} }{2} = 4, -0.25. [/tex]

Since it has to be a positive integer, we get x=4

There are (108)2 ⋅ 100 candies in a store. What is the total number of candies in the store?

Answers

To find the total number of candies, square 108 and then multiply by 100. The steps result in a total of 1,166,400 candies in the store.

Calculating the Total Number of Candies

The expression provided is (108) 2 × 100. To calculate this, first square 108, which means you multiply 108 by itself, and then multiply the result by 100. So the calculation will look like this: 108 × 108 × 100.

To carry out this multiplication, the steps are:

Square 108: 108 × 108 = 11,664.

Multiply the result by 100: 11,664 × 100 = 1,166,400.

Therefore, the total number of candies in the store is 1,166,400.

To find the total number of candies in the store given the expression [tex](108)^2[/tex] times 100, you first square 108 to get 11,664 and then multiply that by 100, resulting in 1,166,400 candies.

The student's question asks for the total number of candies in a store given the expression [tex](108)^2[/tex] times 100.

To find the total, we need to calculate the square of 108 and then multiply the result by 100.

First, 1082 equals 11,664 (108 multiplied by itself).

Next, we multiply 11,664 by 100 to find the total number of candies, which gives us 1,166,400 candies.

Hence, there are 1,166,400 candies in the store.

Step-by-Step Solution:

Calculate the square of 108: 108 x 108 = 11,664.Multiply the result by 100: 11,664 x 100 = 1,166,400.

Therefore, the store has 1,166,400 candies in total.

What do I write for my problem. Reply quickly please

Answers

5.41 is the weight of jim's dog

10.82 is the question mark

16.23 divided into 3 sections would be 5.41

2 sections of the 3 would be 5.41+5.41 = 10.82

Betty had $70. She bought a necklace for $9 and a ring for $7. Which expression correctly shows the total money Betty has left? A $70 − (−$9) + (−$7) B $70 + (−$9) + (−$7) C $70 − (−$9) − (−$7) D $70 + (−$9) − (−$7) A B C D???
PLZZ HELP ASAP

Answers

The correct answer would be B) $70+(-$9)+(-$7) because a negative plus a positive cancels out to make a negative, so even though there is a plus and a minus sign it really only means minus. Therefore, you solve it just like a simple math problem $70-$9-$7. In the end Betty ends up with $54 in total having spend $16.

The answer would be B!

What is 12-(3-1/2)? I NEED ASAP!! THANK YOU

Answers

I believe the answer is 9.5

9.5 because when you subtract 3-1/2 you get 2 1/2 and then you multiply by 12 and get 36 1/2

(-4x^2+3xy-y^2)/-(-7x^2-xy+6y^2)/(x^2+4xy-2y^2)

Answers

Alright, so we can start off by dividing
-4x^2+3xy-y^2 by -(-7x^2-xy+6y^2)=7x^2+xy-6y^2 using long division, getting

-4/7
_____________________
7x^2+xy-6y^2 -4x^2+3xy-y^2
- (-4x^2-4xy/7-24y^2/7)
__________________
25xy/7+31y^2/7

Since we can't do anything at this point, we do
-4/7+(25xy/7+31y^2/7)/(7x^2+xy-6y^2)

At this point, we can divide this by
(x^2+4xy-2y^2), resulting in
(-4/7+((25xy/7+31y^2/7)/(7x^2+xy-6y^2)))/((x^2+4xy-2y^2)). After that, we can't use long division since the numerator's top x exponent is 1.

Answer:

7x+x^-16x+

Step-by-step explanation:

Help!! what is -2r-1= -11

Answers

-2r - 1 = -11

So here you want to group all like terms onto either side.

So you can first do this by getting rid of the -1 by adding 1 instead.

-2r -1 + 1 = -11 + 1

-2r = -10

And then now you can just divide both sides by -2.

-2r = -10

/-2 /-2

r = 5

-2r-1= -11
+1 +1
-2r= -10
r=5

149 x 5 multiply using partial products

Answers

Hi there! Partial products is multiplying each bottom number by the top number. So what did was 9 * 5 = 45. Dropped the five, and carried the 4 to the next number. 5 * 4 + 4 is 24. Drop the 4, and carried the two to the next number. Then I did 5 * 1 + 2 and I got 7. The product of 149 * 5 is 745.

Steve washed 15 cars in 3 hours.how many cars can he Wash in 7 hours?

Answers

15/3 = x/7.

Use cross products and multiply 15*7= 105/3= 35.
He can wash 35 cars in 7 hours..
Hope this helps!
Can u plz mark me as brainliest? I really need it!

Steve washed 15 cars in 3 hours and can wash 35 cars in 7 hours.

We have given that Steve washed 15 cars in 3 hours.

We have to determine if the cars can be Washed in 7 hours.

What is the condition given?

15/3 = x/7.

Use cross products and multiply 15*7

= 105/3

= 35.

He can wash 35 cars in 7 hours

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What value of H makes the equation true

−1/8 x (2H + 4) + 1/2= −7/4

A 7
B 25/16
C 7/16
D 25

Answers

−1/8 x (2H + 4) + 1/2= −7/4
-1/4H - 1/2+ 1/2 = -7/4
-1/4H = -7/4
H = -7/4 * (-4/1)
H = 7
answer
A 7

Which lists these numbers in order from least to greatest?

–14.6, 159, 1.07, –1.295, 24.6

A.
1.07, –14.6, 159, 24.6, –1.295

B.
1.07, –1.295, –14.6, 24.6, 159

C.
–1.295, –14.6, 1.07, 24.6, 159

D.
–14.6, –1.295, 1.07, 24.6, 159

Answers

The answer is D because -14.6 is the least and is the only one that has -14.6 first.

The correct answer is option D –14.6, –1.295, 1.07, 24.6, 159.

Given numbers: –14.6, 159, 1.07, –1.295, 24.6.

To order the numbers from least to greatest, we consider their values:

–14.6 (negative and smallest)–1.295 (negative and larger than –14.6)1.07 (positive and the smallest positive number in this list)24.6 (positive and larger than 1.07)159 (positive and largest)

so,Order from least to greatest is:

–14.6–1.2951.0724.6159

The correct answer is option D –14.6, –1.295, 1.07, 24.6, 159.

Is 500 an underestimate or overestimate for the product of 12 and 53

Answers

Underestimate is the answer

The number 500 is underestimate for the product of 12 and 53.

We need check whether 500 an underestimate or overestimate for the product of 12 and 53.

What is product of numbers?

The product of two numbers is the result you get when you multiply them together.

Now, the product of 12 and 53 is 12 × 53 = 636

An underestimate is an estimate that is less than the actual answer to a problem.

So, the number is underestimated.

Therefore, the number 500 is underestimate for the product of 12 and 53.

To learn more about the product of numbers visit:

https://brainly.com/question/28062408.

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what is the solution to log2(9x)-log2^3=3?

Answers

Answer:

[tex]x = \frac{8}{3}[/tex] is the solution to [tex]\log_2 9x - \log_2 3 = 3[/tex]

Step-by-step explanation:

Using the logarithmic rules:

[tex]\log \frac{m}{n} = \log m -\log n[/tex]

if [tex]\log_b x = a[/tex] then;

[tex]x = b^a[/tex]

Given the equation:

[tex]\log_2 9x - \log_2 3 = 3[/tex]

Solve for x:

Apply the logarithmic rules:

[tex]\log_2 \frac{9x}{3} = 3[/tex]

⇒[tex]\log_2 3x = 3[/tex]

Apply the logarithmic rules;

[tex]3x = 2^3[/tex]

⇒[tex]3x = 8[/tex]

Divide both sides by 3 we have;

[tex]x = \frac{8}{3}[/tex]

Therefore, the solution for the given equations is, [tex]x = \frac{8}{3}[/tex]

Answer: B or option two on edg

X = 8/3

Step-by-step explanation:

An architect is designing a house in which a 104-square-foot room and a 130-square-foot room share a wall. What is the greatest possible integer length of the shared wall?

Answers

I think the answer should be 130 - 104 = 26

how much more is 3/8 gallon than 1/4 gallon?

Answers

1/8 more

1/4 = 2/8

3/8-2/8 =1/8

Francine and Cheryl received equal scores on a test made up of multiple choice questions and an essay. Francine got 34 multiple choice questions correct and received 14 points for her essay. Cheryl got 30 multiple choice questions correct and received 22 points for her essay. How many points was each multiple choice question worth? Enter your answer in the box. 5 points

Answers

34x +14 = 30x +22

34x = 30x + 8

4x =8

x = 8/ = 2

each question was worth 2 points

At a country concert, the ratio of the number of boys to girls is 2:7. If there are 250 more girls than boys, how many boys are at the concert? PLZ HELP

Answers

We can setup an equation for this.

Boys to Girls = 2:7
Boys = x
Girls = 250+x
Setup the ratio
x:(250+x) = 2:7
x / (250+x) = 2/7
7x = 500+2x
7x-2x = 500
x = 500/5 =100

There are 100 boys at the concert

Answer:

100 boys at the concert

Step-by-step explanation:

At a country concert, the ratio of the number of boys to girls is 2:7

Let 'b' be the number of boys in the concert

there are 250 more girls than boys

so b+250 are the number of girls in the concert

the ratio of boys to girls is b: b+250

Now make a proportion using the ratio

[tex]\frac{2}{7} =\frac{b}{b+250}[/tex]

Now solve for b . cross multiply the fraction

[tex](b+250) \cdot 2= 7 \cdot b[/tex]

[tex]2b+500= 7b[/tex]

Subtract 2b from both sides

[tex]5b= 500[/tex]

Divide both sides by 5

b=100

So there are 100 boys at the concert

What property is being used in the equation 3a+0=3a

Answers

the identity of zero

After a 5% sale discount, the price of an item became $38.00. What was the original price?

Answers

0.95x = 38
x = 38/.95
x = 40

Hope this helped!

The answer will be 40 !!

workout 3(-a + 2a - 4)= -5

Answers

Let's solve your equation step-by-step.3(−a+2a−4)=−5Step 1: Simplify both sides of the equation.3(−a+2a−4)=−5(3)(−a)+(3)(2a)+(3)(−4)=−5(Distribute)−3a+6a+−12=−5(−3a+6a)+(−12)=−5(Combine Like Terms)3a+−12=−53a−12=−5Step 2: Add 12 to both sides.3a−12+12=−5+123a=7Step 3: Divide both sides by 3.3a/3=7/3a=7/3Answer:a=7/3

3(-a+2a-4)=-5
3(-a)+3(2a)-3(4)=-5
-3a+6a-12=-5
+12 +12
-3a+6a= 3a
3a=7
--- ---
3 3
a=2.3

what is 11.4 divided by 19

Answers

The answer would be 0.6

the answer should be 0.6

Sasha hikes into a canyon. She takes a break at the rest stations every 2/3 of a mile. If she started at sea level and has hiked down to the fourth rest station, what is Sasha’s elevation now? Select all that apply.

a. -8/3
b. -4 2/3
c. 14/3
d. 2 2/3
e 4/3

Answers

Answer:

a. -8/3 miles below sea level.

Step-by-step explanation:

Sasha started at sea level and has hiked down to the fourth rest station.

Now sea level is 0.

Sasha takes a break at the rest stations every 2/3 of a mile.

This means she is down to 4 rest points means 4 times 2/3

This becomes = [tex]4\times(\frac{2}{3} )=\frac{8}{3}[/tex]

But the answer will be in negative as she is below 0.

So, correct answer is: a. -8/3 miles below sea level.

Shasha's elevation at the fourth rest station is 2 2/3

Position of rest station = 2/3 of a mile

Sea level = 0

The 4th rest station will be located at :

4 × 2/3 = 8/3

Therefore, the position of the fourth rest station from Shasha's starting position is (0 + 8/3) = 8/3

Since, she's hiking upward her position will be 8/3 = 2 2/3

Therefore, Shasha's elevation is

[tex]2 \frac{2}{3} [/tex]

Learn more : https://brainly.com/question/18796573

Two integers, a and b, have a product of 24. What is the least possible sum of a and b?

Answers

The two integers are 6 and 4 because the factors of 24 are 1,2,3,4,6,8,12,24 and 4 and 6 have the smallest sum out of all of them.
1+24=25
2+12=14
3+8=11
4+6=10

What is 53,806 in expanded form using exponents

Answers

5x10^4
+3x10^3
+8x10^2
+0x10^1
+6x10^0

For the problem 135 divided by 5, draw two different ways to break apart the array. Use the Distributive Property to write products for each different way. (Please show picture of arrays!)

Answers

One way of breaking apart the arrays is by partitioning the value 135

135 = 100 + 30 + 5

Then divide each value by 5

135 ÷ 5 = (100 ÷ 5) + (30 ÷ 5) + (5 ÷ 5)
135 ÷ 5 = 20 + 6 + 1
135 ÷ 5 = 27

Another method you can use is shown in the diagram below:

can -60 be a fraction?

Answers

yes [tex] -\frac{60}{1} [/tex]

Yes, any real number can be made into a fraction!
-60 in this case can be made into a fraction by simply putting it over 1. So -60/1 would be it as a fraction.

I will give brainliest to whoever got the right answer first, so please get it right, help me do number 25, number 26, and number 27, remember and please, READ THE DIRECTIONS.

Answers

25. 16x + 9x + 5 = 180 because the angles are supplementary.
25x + 5 = 180
25x = 175
x = 7
Now because there are vertical angles, it is easy to find the value of y.
4y = 9(7) + 5
4y = 63 +5
4y = 68
y = 17

26. 6x - 11 + 2x - 9 = 180 because the angles are supplementary.
8x - 20 = 180
8x = 200
x = 25
Now because there are vertical angles, you can find the value of y.
6(25) - 11 = 20y + 19
150 - 11 = 20y + 19
139 = 20y + 19
120 = 20y
y = 6

27. 9x + 2 + 10x + 7 = 180 because the angles are supplementary.
19x + 9 = 180
19x = 171
x = 9
Again, there are two vertical angles.
10(9) + 7 = 18y + 25
97 = 18y + 25
72 = 18y
y = 4

I really hope this helped you!! :)

16x+9x+5=180
25x=180-5
25x=175
x=175/25
x=7

4y+16(7)=180
4y+112=180
4y=180-112
4y=68
y=17

--------------
26.
6x-11+2x-9=180
8x-20=180
8x=180+20
8x=200
x=25

20y+19 +2(25)-9=180
20y=180+9-19-50
20y=120
y=6

--------------
27.

9x+2+10x+7=180
19x=180-9
19x=171
x=9

9(9)+2+18y+25=180
18y=180-81-25-2
18y=72
y=4

hope this helpsssss

What's a name for 7 over 8

Answers

7/8 is called seven-eights (as a fraction)

hope this helps

As said above, 7/8 or seven-eighths is the name of 7 over 8.

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