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 mi…

Question

asked Nov 14, 2017 14.3k views

2 Answers

Raymond Wang · Answer 1 · 2017-11-20T12:02:36+0000

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.