Question

solve for $x$ and graph the solution on the number line below.
$-1 < x + 8 leq 10$

Explanation:

Step1: Subtract 8 from all parts

Subtract 8 from each part of the compound - inequality:
\(-1-8 < x + 8-8\leq10 - 8\)

Step2: Simplify the expressions

Simplify the left - hand side: \(-1-8=-9\), and the right - hand side: \(10 - 8 = 2\). So we get \(-9 < x\leq2\).

Answer:

The solution of the inequality is \(-9 < x\leq2\). To graph it on a number line, draw an open circle at \(-9\) (because \(x\) is greater than \(-9\) but not equal to it) and a closed circle at \(2\) (because \(x\) is less than or equal to \(2\)), and then draw a line segment connecting the two points.