2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither. You must complete all sections of this questions to receive full credit.
(a) 6x+4x-6=24+9x
(b) 25-4x=15-3x+10-x
(c) 4x+8=2x+7+2x-20

Answers

Answer 1

(a) 6x+4x-6=24+9x

6x+4x-6=24+9x
10x-6=24+9x
x=30
one solution, equation is "neither" identity nor contradiction

(b) 25-4x=15-3x+10-x

25-4x=15-3x+10-x
25-4x=25-4x
both sides are the same (identity)-> infinite solutions

(c) 4x+8=2x+7+2x-20
4x+8=2x+7+2x-20
4x+8=4x-13
8=-13
no solutions -> Contradiction

Answer 2

Final answer:

In equation (a), x=30 is the solution. In equation (b), it has an infinite number of solutions. In equation (c), it has no solution.

Explanation:

(a) To solve the equation 6x+4x-6=24+9x, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

10x-6=24+9x

Next, move all the terms with x to one side of the equation by subtracting 9x from both sides:

10x-9x-6=24

Simplify further:

x-6=24

Now, isolate x by adding 6 to both sides:

x-6+6=24+6

x=30

Therefore, the equation has one solution, x=30.

(b) To solve the equation 25-4x=15-3x+10-x, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

25-4x=15-3x+10-x

Combine like terms:

25-4x=25-4x

Notice that both sides of the equation are identical. This means that the equation is an identity, and it has an infinite number of solutions.

(c) To solve the equation 4x+8=2x+7+2x-20, we need to simplify both sides of the equation and isolate the variable x. Start by combining like terms on both sides of the equation:

4x+8=2x+7+2x-20

Combine like terms:

4x+8=4x-13

Notice that both sides of the equation are not equal. This means that the equation is a contradiction, and it has no solution.

Learn more about Solving equations here:

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Related Questions

It is a commonly used guideline that for the average American child, their maximum adult height will be about twice their height at age 2. Suppose that Micah’s adult height fits the following equation a = 2c – 1, where a represents his adult height and c represents his height at age 2. At age 2 Micah was 35 inches tall. What is Micah’s adult height? Write and solve an equation.

Answers

a=2c-1
a=2(35in)-1
a=70-1
a=69in.

Final answer:

The question is about predicting Micah's adult height based on his height at the age of 2. Using the formula a=2c-1 where 'c' is the height at age 2, we substitute 'c' with 35 (his height at age 2) and calculate. Thus, Micah's adult height is predicted to be 69 inches.

Explanation:

The question asks about Micah's adult height based on the given equation, a = 2c – 1. In this equation, 'a' represents Micah's adult height and 'c' represents his height at age 2. Given that Micah's height at age 2 ('c') is 35 inches, we can substitute this value into the equation to find Micah's adult height ('a').

So, substituting c=35 into the equation gives us: a = 2*35 - 1. Calculating this results in: a = 70 - 1. Therefore, Micah's adult height is predicted to be 69 inches.

Learn more about Height prediction here:

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Evaluate A2 for A = -3.

-9
-6
6
9

Answers

A^2

-3^2 = 9

the answer is 9

What would be the third step in simplifying the expression 4 2 ÷ (2 · 9) + 5?
divide
exponent
add
multiply

Answers

P
E
M
D
A
S

okay since the first step is parenthesis, the next step would be exponents but you have none so you skip to multiplication, then you divide

divide is your answer

A machine produces 75 widgets an hour. How many widgets does it produce in 6 minutes

Answers

The answer is 12.5 because 75 divided by 6 is 12.5

The machine produces 7.5 widgets in 6min.

75 widgets/hr
60min = 1hr

75/60=1.25 so 1.25 widgets/min

1.25•6=7.5 widgets/6min.

simplify the expression 3^-2/3^-4

Answers

3^-2/3^-4 is = 9 wow that was hard XD

Applying the Power Rule: [tex]x^m[/tex]÷[tex]x^n[/tex] = [tex]x^{m-n}[/tex]

[tex]3^{-2}[/tex]÷[tex]3^{-4}[/tex] = [tex]3^{-2--4}=3^{-2+4}=3^2=9[/tex]

What is 12.405 as a mixed number in simplest form

Answers

Final answer:

To express 12.405 as a mixed number in simplest form, the whole number part is 12, and the decimal .405 is equivalent to 405/1000, which simplifies to 81/200, resulting in the mixed number 12 81/200.

Explanation:

To express the decimal 12.405 as a mixed number, we first recognize that the number to the left of the decimal point is the whole number part, which is 12. The decimal part is .405, which we need to convert to a fraction. Since .405 has three decimal places, it is equivalent to 405/1000. However, we must simplify this fraction to its simplest form.

We find the greatest common divisor (GCD) of 405 and 1000, which is 5. Dividing both numerator and denominator by 5, we get 81/200. Thus, the mixed number equivalent of 12.405 in simplest form is 12 81/200.

An important note to consider is that when working with significant figures, the number of decimal places in the original number is maintained in the fractional part of the mixed number. Therefore, in a scientific context, the number of significant figures can influence the final result.

I CANT FIGURE OUT HELP ME!!! SOLVE FOR W: −(14w+8)+8=3

IM GIVING MAX POINTS I CAN!!!!!

Answers

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves.

The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6
Now let's solve the equation you provided.

−(1\4w+8) + 8 = 3
-1\4w - 8 + 8 = 3 <-- Distribute the negative sign
-1\4w = 3 <-- Combine like terms
w = 3 ÷ [tex] -\frac{1}{4}[/tex]
w = -12

So, w is equal to -12.

-12 is the answer!
BOOM! lol

Which number is prime? Choose each correct answer. 55 56 57 58 59 60 61

Answers

59 and 61 are prime
answerss

The prime numbers are 59 and 61

A ship is 2.2° off course. If the ship is traveling at 18.0 miles per hour, how far off course will it be after 5 hours?

Answers

___x____
\ |
\ |
\ | y
18 \ |
\ |
\ *|---2.2 °

This is a vector problem. The distance of drift is in x (horizontal axis).
remember that Sin Ф=opposite/hypotenuse. x represents the opposite side form the angle, and 18 is the hypotenuse.
Sin 2.2°=x/18
18 sin 2.2°=x
.691 ≈x

The ship drifts off course .691 miles every hour. .691 x 5 = 5.69 miles after 5 hours.

Final answer:

To determine how far off course a ship will be after 5 hours traveling at 18.0 mph and being 2.2° off course, use the formula: Distance off course = 18.0 mph x 5 hours x sin(2.2°). This results in the ship being approximately 3.45 miles off course after 5 hours.

Explanation:

To calculate how far off course the ship will be after 5 hours, we first need to find the distance the ship travels while off course.

Distance off course = 18.0 mph x 5 hours x sin(2.2°).

Distance off course ≈ 3.45 miles.

what is the answer to the equation -7+x=6x-12 ?

Answers

-7 + x = 6x - 12

-7 +12 = 6x - x

5 = 5x

x = 1

hope this helps

-7+x=6x-12
-x -x
-7=5x-12
+12 +12

5=5x
X=1

Y times y of the power to 4

Answers

y * y^4 = y^5

Remember that y equals y^1. Also when multiplying exponents with the same base, add the given exponents. 1+4=5

Final answer: y^5

one third of a number

Answers

Well the thing is you didn't tell us which number but if it is 12 then i strongly believe that the answer is 3/9

One third of a number is same as n/3 or 1/3 · n

What is the value of y?

Answers

64............................

well you know no matter what a triangle will always equal 180 degrees so you take 37 + 79 and you get 116 which you then subtract from the 180 you know a triangle will always be and you will get y=64

Richie has 27apple he buys 12 more apples how many apples does he have how ?

Answers

27 + 12
39

Hope this helps!

Richie has 39 apples

What is a multiplication story for 2x6=

Answers

2x*6=
x=12
2*6=12
But either way. I think that's the answer

6/20
3/15
15/20
16/32
21/45
Simplest form please

Answers

3/10
1/5
3/4
1/2
7/15
Thanks (:

Salutations!

To simplify fractions, you can either do the prime factorization method, or find the same factors for the simplified numbers.

6/20 = 3/10

3/15 = 3/5

15/20 = 5/6

16/32 = 1/4

21/45 = 7/15.

Hope I helped (:

Have a great day!

How do I do this (Comes With Picture) if someone could help me with this that would be amazing :)

Answers

The error occurs in step 3. The student did not distribute the negative properly to every term inside the parenthesis. Below is one proper way to solve for y

[tex]3 - \left(y + \frac{1}{2}\right) = 8[/tex]

[tex]3-3 - \left(y + \frac{1}{2}\right) = 8-3[/tex]

[tex]-\left(y + \frac{1}{2}\right) = 5[/tex] <--- Note the negative and the parenthesis

[tex]-y - \frac{1}{2} = 5[/tex] <--- Note how we have -1/2 and not +1/2

[tex]-y - \frac{1}{2}+\frac{1}{2} = 5+\frac{1}{2}[/tex]

[tex]-y = 5\frac{1}{2}[/tex]

[tex]y = -5\frac{1}{2}[/tex]

So the proper final answer is [tex]y = -5\frac{1}{2}[/tex]
(this is a mixed number which converts to the decimal number -5.5)

Jeanie has a 3/4 piece of ribbon. She needs one 3/8 yard piece and a 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Explain

Answers

Jeanie cannot cut the piece of ribbon into two smaller pieces.

[tex] \frac{3}{4} = \frac{6}{8} [/tex] if you multiply the numerator and the denominator for [tex] \frac{3}{4} [/tex] by 2.
She needs [tex] \frac{1}{2} [/tex] yard piece, which is [tex] \frac{4}{8} [/tex] if you multiply the numerator and the denominator for [tex] \frac{1}{2} [/tex].
Now that all the numbers have the same denominator, you can subtract the numerators which is: 6 - 4 - 3 = -1
This means that she cannot cut the ribbon into two smaller pieces.

~I hope this helped!!

Which table best represents the steps to solve the equation 8 + = 4?

Answers

Usaully if you add a larger number with a smaller negative number you will get your answer is 8 + -4+4

Solve: 2x + 12 - 7x = -2

Answers

x=14 over 5 that's the answer I got when I did it on paper

2x + 12 - 7x = -2
1. you can either minus or add 7x to 2x
2. which gives 9x + 12 = -2
3. minus 12 on both sides
4. gives you 9x +-14
5. divided -14 by 9

Answer is -1.55 repeatting

how to convert unit rates

Answers

When you talk about the speed of a car, you usually say something in miles per hour. For example, you say, 'I drove 40 miles per hour.' Normally, you don't say, 'I drove 120 miles per 3 hours.' Figure out how to convert a rate like 120 miles per 3 hours to theunit rate of 40 miles per hour by watching this tutorial.

To find 12 times 13, I double 13 and halve 12 and then multiply

Answers

No just multiply them 12 times 12 is 144 just add 12 so it could be 12 times 13 and it would be 156

13
x12
——-
26
+130
——-
156

So first you do the back of 12, 2 times the back of 13, which is 6. Then the back of 12, 2 times the front of 13, which is 2. So you get 26. Then you go to the next line and put a zero, then the same thing as you did with the back of 12, but with the front, which is 1. So 1 times 3 and 1 times 1, so you get 13 and the zero you added earlier, 130. So you get 26 and 130, add them to get 156.

a
22 degrees

b
3 degrees

c
40 degrees

d
20 degrees

Answers

Bisects means it divides in two equal parts. So:

7x - 1 = 4x + 8
3x = 9
x = 3

This problem isn't over, though.

7(3) - 1
20

Because one of the parts equals 2, the whole thing equals double of that, or 40

Hope this helps!

the answer is d.

7x-1=4x+8

3x-1=8

3x=9
x=3

7(3)-1=20°

A sidewalk is built 12 bricks wide by laying each brick side by side. How many inches wide is this seidewalk if each brick measures 3 7 over 8 inches wide ??

Answers

1 brick = 37/8
37/8 x 12 = 55.5 inches wide

Hope this helps!! :)

indira, bonnie and chang all work at the same pet store. indira works every other day. bonnie works every fourth day. chang works every fifth day. today they all work together. how many days will it be until they work together again?

Answers

This is asking for the LCM between 2,4, and 5. It is 20. So, the answer is 20 days.

Hope this helps!

Please help me on number 12 :)

Thank you ! :)

Answers

2 divided by 5

2/5

Hope i helped =)

Selena bought 5.62 pounds of meat for $3.49 per pound. What was the total cost of the meat?

Answers

Pounds multiplied by the unit price will solve this problem. Be sure to round your answer to two decimal places; it's money $.

5.62 lbs x $3.49/lb = $19.61

Simply multiply 5.62lb by $3.49/lb = 19.6138 or 19.61 in short form.

Express 42 and 150 as a product of its prime numbers.

Answers

42 = 3 x 2 x 7

150 = 5 x 5 x 3 x 2

hope this helps

10 power of 1 x 0.23

Answers

10^1=10
10x0.23=final answer=2.3

PLEASE HELP- Anna has 10 tee shirts and 7 pairs of shorts that she either wears with sandals or sneakers if all the colors and patterns coordinate, how many different outfits can Anna make?

THANK YOU!!

Answers

Anna can make about 6 different outfits

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