Question

solve the compound inequality. 2x - 5 < 1 and 2x + 6 ≥ - 2 graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 5 to both sides of $2x - 5 < 1$.
$2x-5 + 5<1 + 5$
$2x<6$
Divide both sides by 2: $x < 3$.

Step2: Solve the second inequality

Subtract 6 from both sides of $2x+6\geq - 2$.
$2x+6 - 6\geq - 2-6$
$2x\geq - 8$
Divide both sides by 2: $x\geq - 4$.

Answer:

The solution of the compound - inequality is $-4\leq x < 3$. On the number - line, we mark a closed circle at $x = - 4$ (because $x$ can equal $-4$) and an open circle at $x = 3$ (because $x$ cannot equal 3) and draw a line segment connecting them.