Question

solve for d.
$-2(2d - 19) \leq 4 + 2d - 8$
write your answer using a decimal, whole number, or fraction in lowest terms.

Explanation:

Step1: Simplify both sides

Left: $-2(2d - 19) = -4d + 38$
Right: $4 + 2d - 8 = 2d - 4$
Inequality becomes: $-4d + 38 \leq 2d - 4$

Step2: Move d terms to left

Subtract $2d$ from both sides:
$-4d - 2d + 38 \leq -4$
$\implies -6d + 38 \leq -4$

Step3: Isolate constant terms

Subtract 38 from both sides:
$-6d \leq -4 - 38$
$\implies -6d \leq -42$

Step4: Solve for d, reverse inequality

Divide by $-6$ (reverse inequality sign):
$d \geq \frac{-42}{-6}$
$\implies d \geq 7$

Answer:

$d \geq 7$