Question

What is the solution to –2(5y – 5) – 3y ≤ –7y + 22?

A. y ≤ 2
B. y ≥ –2
C. y ≥ –10
D. y ≤ –20

Answer 1

-2(5y - 5) - 3y < = -7y + 22
-10y + 10 - 3y < = -7y + 22
-13y + 10 < = -7y + 22
-13y + 7y < = 22 - 10
-6y < = 12
y > = -12/6
y > = -2....answer B

Answer 2

Option: B is the correct answer.

y≥ -2

Explanation:

We are asked to find the solution of the inequality:

–2(5y – 5) – 3y ≤ –7y + 22.

We will solve for the inequality as:

-2×5y-2×(-5)-3y ≤ -7y+22 (on solving for the parantheses in the left hand side of the inequality)

-10y+10-3y ≤ -7y+22

⇒ -10y+7y-3y ≤ 22-10 (on combining the like terms)

⇒ -6y ≤ 12

⇒ y≥ -2 (on dividing both side by -6 also the sign of the inequality changes as the negative sign is treated on both the side)

Hence option: B is the correct answer.

y ≥ -2.