Word problem

Question

Given the equation 7(x + 2) = 2x − 1, solve for the variable. Explain each step and justify your process.
Jeff solved a similar equation below. Is Jeff's solution correct? Explain why or why not.
3x − 2 = 5(x + 2)
3x − 2 = 5x + 10
8x = 8
x = 1

Answer 1

7(x+2)=2x-1

clear the parentheses by multiplying through the 7

 

7x+7(2)=2x-1

7x+14=2x-1

subtract 2x from both sides to get all the variables together.

7x-2x+14=2x-2x-1

5x+14=-1

subtract 14 from both sides to isolate the variable

5x+14-14=-1-14

5x=-15

divide both sides by 5

(5x)/5=(-15)/5

x=-3

 

For Jeffs problem his answer is incorrect.

 

3x-2=5(x+2)

3x-2=5x+10.   at this point Jeff is correct.

 

When Jeff tried to move the 5x to the left side of the equation, it had to be subtracted from both sides... Jeff subtracted 5x from the right side and added 5x to the left.  Also when Jeff wanted to move the -2 from the left side to the right side we had to add 2 to both sides of the equation.  Jeff added on the left side and subtracted 2 on the right.

 

-5x+3x-2+2=5x-5x+10+2 gives

-2x=12 not 8x=8

 

From -2x=12 divide both sides by -2

(-2x)/(-2)=12/(-2)

x= -6      NOT   x=1