Question

1. which number line represents the solution to the inequality 5 - 3x < 11? clear all

Explanation:

Step1: Solve the inequality

Starting with \(5 - 3x<11\), subtract 5 from both sides: \(5-3x - 5<11 - 5\), which simplifies to \(-3x<6\).

Step2: Isolate \(x\)

Divide both sides of \(-3x<6\) by - 3. When dividing an inequality by a negative number, the direction of the inequality sign changes. So \(\frac{-3x}{-3}>\frac{6}{-3}\), resulting in \(x > - 2\).

Step3: Interpret on number - line

On a number - line, \(x>-2\) is represented by an open circle at - 2 (because \(x\) is strictly greater than - 2, not equal to) and an arrow pointing to the right.

Answer:

The number - line with an open circle at - 2 and an arrow pointing to the right represents the solution.