Question

8 solve the inequality and graph the solution. -6(1 + 4x) < -30

Explanation:

Step1: Divide both sides by -6

When dividing an inequality by a negative number, the inequality sign flips. So we have \(\frac{-6(1 + 4x)}{-6}>\frac{-30}{-6}\), which simplifies to \(1 + 4x>5\).

Step2: Subtract 1 from both sides

Subtract 1 from each side: \(1 + 4x-1>5 - 1\), which gives \(4x>4\).

Step3: Divide both sides by 4

Divide both sides by 4: \(\frac{4x}{4}>\frac{4}{4}\), so \(x > 1\).

Answer:

The solution to the inequality \(-6(1 + 4x)<-30\) is \(x>1\). For the graph, it would be an open circle at \(x = 1\) on the number line and an arrow pointing to the right (towards positive infinity) to represent all values of \(x\) greater than 1.