Question

[02.05] Marcie solved the following inequality, and her work is shown below: −2(x − 5) − 12 ≤ 4 + 6(x + 3) −2x + 10 − 12 ≤ 4 + 6x + 18 −2x − 2 ≤ 6x + 22 −8x ≤ 24 x ≤ −3 What mistake did Marcie make in solving the inequality?

Answer 1

Hi there! Marcie made a mistake in the last step of the solving process.

Let's solve this problem step by step!
−2(x − 5) − 12 ≤ 4 + 6(x + 3)

First work out the parenthesis, which can for instance be done using rainbow method.

−2x + 10 − 12 ≤ 4 + 6x + 18
The parenthesis are worked out correctly. Remember that multiplying a negative by a negative gives you a positive.

Now we can collect the terms.
−2x − 2 ≤ 6x + 22

The terms are collected correctly.

Next up is subtracting 6x from both sides and adding 2 to both sides of the inequality.
−8x ≤ 24

This step is also correct.
Finally we must divide both sides of the inequality by -8 to find our answer. Be aware of the fact that the sign flips when dividing by a negative!

x ≤ −3
Mistake! Marcie forgot to flip the sign. Instead the answer should be $x \geqslant - 3$

~ Hope this helps you!