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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?

She subtracted 6x from both sides when she should have added 2x.
She added 2 to both sides when she should have subtracted 22.
When dividing by −8, she did not change the ≤ to ≥.
She did not make a mistake.

Respuesta :

esme15
She didn't make any mistake

Answer:

When dividing by −8, she did not change the ≤ to ≥

Step-by-step explanation:

Marcie solved the following inequality

[tex]-2(x -5) - 12 \leq  4 + 6(x + 3)[/tex]

-2 and 6 is distributed inside the parenthesis and did it correctly

[tex]-2x + 10 - 12 \leq 4 + 6x + 18[/tex]

Like terms are combined and it is correct.

[tex]-2x - 2 \leq  6x + 22[/tex]

Like terms are combined further

[tex]-8x \leq 24[/tex]

When we divide or multiply an inequality by a negative number then we change the inequality sign.

[tex]x \geq -3[/tex]

When dividing by −8, she did not change the ≤ to ≥