Question

Solve the inequality $\mathbf{3}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{>}\mathbf{-}\mathbf{11}$, express the solution using interval notation and graph the solution set on real number line.

Short answer

The solution of the inequality$3x-2>-11$ is$x>-3$ whose interval notation is $x\in \left(-3,\infty \right)$and graph is shown on real number line.

Step-by-step solution

Step 1. Solve the given inequality.

$\begin{array}{c}3x-2>-\mathrm{11....}\left(\text{Given}\right)\\ 3x>-11+\mathrm{2....}\left(\text{Add2bothsides}\right)\\ 3x>-9\\ x>-3\end{array}$

Step 2. Writing interval notation and graph of solution on real number line.

The interval notation for$x>-3$ is written as $x\in \left(-3,\infty \right)$.

The graph of solution on real number line is shown below.

Step 3. DESCRIPTION OF STEPS.

The solution of the inequality is$x>-3$ whose interval notation is $x\in \left(-3,\infty \right)$.