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

 
The original equation:                          7(x + 2) = 2x − 1

Eliminate parentheses on the left:        7x + 14 = 2x - 1

Subtract  2x  from each side:                5x + 14 = -1

Subtract  14  from each side:                5x         = -15

Divide each side by  5 :                          x          = -3

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Jeff thought he had solved a similar equation, but his solution is not correct.

Here are his steps, with my commentary:

3x − 2 = 5(x + 2)            The original equation, to be solved.

3x − 2 = 5x + 10            Eliminated parentheses on the right, correctly.

8x = 8                            Subtracted  5x from each side, incorrectly. 
                                      Left side should be  -2x, not  8x .
                
                                     Added  2  to each side, incorrectly.
                                     Right side should be  12, not  8.
                                     
x = 1                            Divided each side by  8, correctly.
                                    But the input from the previous step was garbage,
                                    so the output from this one is garbage.


Jeff should have taken a moment to check his solution,
back in the original equation.

The original equation:            3x − 2 = 5(x + 2)         

If  x = 1, then                       3(1) - 2  =  5 (1 + 2) 

                                               3  -  2  =  5 (3)

                                                     1    =  15            I'm afraid not.
                                                                               Poor Jeff.