Question

an inequality is shown. 4x - 25 > 9x + 5. solve the inequality and graph the solution on the number line.

Explanation:

Step1: Move like - terms to one side

Subtract \(4x\) from both sides: \(4x - 25-4x>9x + 5-4x\), which simplifies to \(-25>5x + 5\).

Step2: Isolate the term with \(x\)

Subtract 5 from both sides: \(-25 - 5>5x+5 - 5\), getting \(-30>5x\).

Step3: Solve for \(x\)

Divide both sides by 5: \(\frac{-30}{5}>\frac{5x}{5}\), so \(x < - 6\).

Answer:

The solution of the inequality is \(x < - 6\). On the number - line, you would use an open circle at \(-6\) (since the inequality is strict, \(x
eq - 6\)) and shade the line to the left of \(-6\).