Question

solve the compound inequality, -14<2x - 4<2. graph the solution on the number line.

Explanation:

Step1: Solve left - hand side of inequality

Add 4 to both sides of $-14 < 2x - 4$. We get $-14+4<2x-4 + 4$, which simplifies to $-10 < 2x$. Then divide both sides by 2: $\frac{-10}{2}<\frac{2x}{2}$, so $- 5

Step2: Solve right - hand side of inequality

Add 4 to both sides of $2x - 4 < 2$. We get $2x-4 + 4<2 + 4$, which simplifies to $2x<6$. Then divide both sides by 2: $\frac{2x}{2}<\frac{6}{2}$, so $x < 3$.

Step3: Graph on number line

Draw a number line. Mark - 5 and 3 with open circles (because the inequalities are strict, i.e., $<$ not $\leq$). Shade the region between - 5 and 3.

Answer:

The solution of the compound inequality is $-5 < x < 3$. On the number line, mark open - circles at $x=-5$ and $x = 3$ and shade the region between them.