# 2. Solve the equation and show your work. 6x + 4x - 6 = 24 + 9x

## Answers

1)sister-x

kim will represent 2x

x+2x=36

3x=36

x=12

2x=24

Kim is 24 years old and her sister is 12 years old.

3).3x will represent tanya and 4y will represent tony.

3x=4(x-2.25)

3. c x 3 = 4

c x 3/3 = 4/3 ( Use the inverse of operation and divide both sides of the equation to isolate the variable)

c = 4/3

c = 1.333333333, 3/4 = 0.75

a. infinite solutions, answer is x = 30, identity equation

b. no solution, a contradiction equation

c. no solution, a contradiction equation

Step-by-step explanation:

Well if I did the right calculations... Kim is 24. The sister is age twelve! Hope I helped.

A. K+S=36

B. Well Simple Addition and Subtraction solves this easily. If you Add 12+12 it equals 24. It still needs to be larger so that Kim is twice as old as her little sister. So you Add another 12 which gives you 36. Or you can easily subtract 12 from it and that will also bring you to 24.

A)

6x + 4x - 6 = 24 + 9x

10x - 6 = 24 + 9x

2x = 24 + 6

x = 15

x has one solution.

b)

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

x has no solution.

c)

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

0x = -13 - 8

0x = -21

x is undefined.

x ≠ ∞ or x ≠ -∞

∴ x has no solution.

A) 6x + 4x - 6 = 24 + 9x

10x - 9x = 24 + 6

x = 30

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

25 - 4x = 25 - 4x

Infinite Solutions.

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

4x - 4x = 7 - 20 - 8

0 = - 22

No solution

Kim is 24 and her sister is 12

Use the acronym DCOAM [Distribute, Combine like terms, one side the variable, Add or subtract, Multipy or divide]

A has only one solution , x= 30

B is an identity because if you combine like terms and add, you get

25-4x=25-4x

C has no solutions

x=30

Step-by-step explanation:

First combine like terms.

10x-6=24+9x

Thenget ride of the 9x which you would subtract it from each side.

10x -9x 9x-9x

Then it will leave you with 1x-6=24

Then add 6 to both side which will canvel out the -6.

Which leads you to 1x =30, all you have to do now is dived both sides by 1 and the answer is 30

[tex]2. Solve the equation and show your work. 6x + 4x - 6 = 24 + 9x[/tex]