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

The mistake which Marcie made in solving the equation was when she added 2 to 6x and 2 to 22 to make ≤ 24. x ≤ −3.

Adding 2 to 6x would make 6x + 2, therefore this is the mistake that Marcie made solving the inequality.

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.