Question: Solve \(3x + 4 \leq 6x - 11\) Put your solution on a number line.

Solve \(3x + 4 \leq 6x - 11\)

Put your solution on a number line.

Solution

Step 1: Subtract \(3x\) from both sides of the inequality. \[ 3x + 4 - 3x \leq 6x - 11 - 3x \] \[ 4 \leq 3x - 11 \] Step 2: Add \(11\) to both sides of the inequality. \[ 4 + 11 \leq 3x - 11 + 11 \] \[ 15 \leq 3x \] Step 3: Divide both sides of the inequality by \(3\). \[ \frac{15}{3} \leq \frac{3x}{3} \] \[ 5 \leq x \] The solution on a number line is represented as all real numbers \(x\) such that \(x\) is greater than or equal to \(5\). This is shown by a closed circle at \(5\) and a shading extending to the right.