Question

solve the inequality. -1 ≤ -2d + 7 < 10 solution : graph the solution.

Explanation:

Step1: Subtract 7 from all parts

Subtract 7 from each part of the compound - inequality $-1\leq - 2d + 7\lt10$.
We get $-1-7\leq - 2d+7 - 7\lt10 - 7$, which simplifies to $-8\leq - 2d\lt3$.

Step2: Divide all parts by - 2

When dividing an inequality by a negative number, the direction of the inequality signs changes.
Dividing $-8\leq - 2d\lt3$ by - 2 gives $\frac{-8}{-2}\geq\frac{-2d}{-2}>\frac{3}{-2}$, which simplifies to $4\geq d>-\frac{3}{2}$ or $-\frac{3}{2}\lt d\leq4$.

Answer:

$-\frac{3}{2}\lt d\leq4$; The graph has an open - circle at $-\frac{3}{2}$ (because $d>-\frac{3}{2}$) and a closed - circle at 4 (because $d\leq4$) with a line segment connecting them.