Question

solve the compound inequality. 2x - 6 < -4 or 4x + 4 ≥ 28 graph the solution on the number line.

Explanation:

Step1: Solve the first inequality

Add 6 to both sides of $2x - 6 < - 4$:
$2x-6 + 6< - 4+6$, which simplifies to $2x<2$. Then divide both sides by 2: $x < 1$.

Step2: Solve the second inequality

Subtract 4 from both sides of $4x + 4\geq28$:
$4x+4 - 4\geq28 - 4$, which simplifies to $4x\geq24$. Then divide both sides by 4: $x\geq6$.

Step3: Graph on number - line

For $x < 1$, we use an open circle at 1 and shade to the left. For $x\geq6$, we use a closed circle at 6 and shade to the right.

Answer:

The solution of the compound inequality is $x < 1$ or $x\geq6$. On the number - line, there is an open circle at 1 with shading to the left and a closed circle at 6 with shading to the right.