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.