Question

solve the linear inequality for w. write your answer in inequality notation. 2(-w - 40) + 40 ≥ 3w - 20

Explanation:

Step1: Expand left-hand side

$2(-w - 40) + 40 = -2w - 80 + 40 = -2w - 40$

Step2: Rewrite inequality

$-2w - 40 \geq 3w - 20$

Step3: Move w terms to left

$-2w - 3w - 40 \geq -20$

Step4: Simplify left w terms

$-5w - 40 \geq -20$

Step5: Move constant to right

$-5w \geq -20 + 40$

Step6: Simplify right-hand side

$-5w \geq 20$

Step7: Divide by -5, flip inequality

$w \leq \frac{20}{-5}$

Step8: Calculate final value

$w \leq -4$

Answer:

$w \leq -4$