Question

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

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Answer 2

All steps that Marcie did are right, but she forgot to change sign in last step.

Consider the inequality

`-2(x - 5) -12 \le 4 + 6(x + 3).`

Then

`-2x+10-12 \le 4 + 6x+18.`

Group the numbers:

`-2x-2 \le 6x+22.`

Separate terms with x and without x in different sides:

`-2x-6x \le 22+2.\\-8x\le 24.`

The coefficient at x is -8 and it is negative, then dividing the inequality by -8 you have to change sign in opposite:

`x\ge -3.`

Answer: Marcie forgot to change sign in last step.