Question

graph the solution to the inequality on the number line. |4x - 6| ≤ 10

Explanation:

Step1: Remove absolute - value

We know that if \(|a|\leq b\) (\(b\geq0\)), then \(-b\leq a\leq b\). So for \(|4x - 6|\leq10\), we have \(- 10\leq4x - 6\leq10\).

Step2: Solve the left - hand side of the compound inequality

Add 6 to all parts: \(-10 + 6\leq4x-6 + 6\leq10 + 6\), which simplifies to \(-4\leq4x\leq16\).

Step3: Solve for \(x\)

Divide all parts by 4: \(\frac{-4}{4}\leq\frac{4x}{4}\leq\frac{16}{4}\), so \(-1\leq x\leq4\).

Step4: Graph on number line

On the number line, we mark a closed - circle at \(x=-1\) and \(x = 4\) (because the inequality is \(\leq\)), and shade the region between them.

Answer:

On the number line, mark closed - circles at \(x=-1\) and \(x = 4\) and shade the region between them.