Question

Marcie solved the following inequality, and her work is shown below:

−2(x − 5) ≤ 6x + 18
−2x + 10 ≤ 6x + 18
−8x +10 ≤ 18
−8x ≤ 8
x ≤ −1

What mistake did Marcie make in solving the inequality?

She subtracted 6x from both sides when she should have added.
She subtracted 10 from both sides when she should have added.
She did not make a mistake.
When dividing by −8, she did not change the direction of the sign.

Answer 1

When dividing an inequality with a negative value , the inequality sign changes direction.

The original Less than or equal to sign should heave been changed to greater than or equal to.

The answer is: When dividing by −8, she did not change the direction of the sign.

Answer 2

The mistake that Marcie made was that, when dividing by -8, she did not change the direction of the sign.

What are inequalities and how to solve them?

Inequalities are what equations aren't. They have inequality symbols instead of equality symbols.

When solving an inequality, the operations such as addition and subtraction are treated the same way as with equalities. But when a negative number is multiplied or divided, the inequality sign is reversed.

We can find the mistake in Marcie's solution as shown below:

Marcie's solution is given below:

−2(x − 5) ≤ 6x + 18

−2x + 10 ≤ 6x + 18

−8x +10 ≤ 18

−8x ≤ 8

x ≤ −1

This can be corrected as shown below:

−2(x − 5) ≤ 6x + 18

−2x + 10 ≤ 6x + 18

−8x +10 ≤ 18

−8x ≥ 8

x ≥ −1

We can see that the sign was reversed. So, the mistake that Marcie made was that she forgot the inequality sign of the inequality when she divided it by a negative number.

Therefore, we have found that the mistake that Marcie made was that, when dividing by -8, she did not change the direction of the sign. The correct answer is option D.

Learn more about inequalities here: https://brainly.com/question/24372553

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