Question

solve and graph the following inequality: $-2 - 9x leq 9x + 4$

Explanation:

Step1: Move variables to one side

Add \(9x\) to both sides: \(-2-9x + 9x\leq9x + 4+9x\), which simplifies to \(-2\leq18x + 4\).

Step2: Isolate the term with \(x\)

Subtract \(4\) from both sides: \(-2-4\leq18x+4 - 4\), so \(-6\leq18x\).

Step3: Solve for \(x\)

Divide both sides by \(18\): \(\frac{-6}{18}\leq\frac{18x}{18}\), which gives \(x\geq-\frac{1}{3}\).

Answer:

\(x\geq-\frac{1}{3}\)

To graph \(x\geq-\frac{1}{3}\) on a number line:

• Place a closed circle (because the inequality is \(\geq\)) at \(-\frac{1}{3}\).
• Shade to the right of \(-\frac{1}{3}\) to represent all values of \(x\) that satisfy the inequality.