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

βˆ’2(x βˆ’ 5) βˆ’ 12 ≀ 4 + 6(x + 3)
βˆ’2x + 10 βˆ’ 12 ≀ 4 + 6x + 18
βˆ’2x βˆ’ 2 ≀ 6x + 22
βˆ’8x ≀ 24
x ≀ βˆ’3

What mistake did Marcie make in solving the inequality? (2 points)


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 βˆ’8, she did not change the ≀ to β‰₯.

She did not make a mistake.

Respuesta :

Answer:

She forgot to flip the inequality when dividing by a negative

Step-by-step explanation:

βˆ’2(x βˆ’ 5) βˆ’ 12 ≀ 4 + 6(x + 3)

Distribute the -2 and the 6

-2x+10 -12 ≀ 4 + 6x + 18

Combine like terms

-2x-2 ≀ Β 6x+22

Subtract 6x from each side

-2x-6x-2 ≀ Β 6x-6x+22

-8x-2 ≀ +22

Add 2 to each side

-8x-2+2 ≀ +22+2

βˆ’8x ≀ 24

Divide by -3. Β Remember when multiplying or dividing by a negative to flip the inequality

-8x/-8 β‰₯ 24/-8

xβ‰₯-3