Question

Andrew solved the following inequality, and his work is shown below:

−4(x + 8) + 25 ≤ −2 + 1(x − 50)
−4x − 32 + 25 ≤ −2 + 1x − 50
−4x − 7 ≤ 1x − 52
−5x ≤ −45
x ≤ 9
What mistake did Andrew make in solving the inequality?

Answer 1

Andrew failed to change the direction of the inequality

Explanation:

You want to know the mistake in Anderw's work solving the inequality ...

−4(x + 8) + 25 ≤ −2 + 1(x − 50)

Solution

−4(x + 8) + 25 ≤ −2 + 1(x − 50)

−4x − 32 + 25 ≤ −2 + 1x − 50

−4x − 7 ≤ 1x − 52

−5x ≤ −45

x ≥ 9

Andrew's mistake was failing to reverse the inequality symbol when dividing by a negative number (-5) at the last step.

__

Additional comment

The last steps of the solution could be written ...

-5x ≤ -45

45 ≤ 5x . . . . . . . add 5x+45 to both sides

9 ≤ x . . . . . . . . . divide by 5 (no reversal of ≤ is needed)