Question

Solve each inequality. Describe the solution set using set builder or interval notation. Then graph the solution set on a number line.

$\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{4}\ge \mathbf{19}$

Short answer

Solution set of inequality is $\mathbf{[}\mathbf{5}\mathbf{,}\mathbf{+}\infty \mathbf{)}$.

Solution set on number line is

Step-by-step solution

- Write properties of inequality.

Properties of inequalities are written in following table:

- Solve 3x+4≥19.

To solve given inequality, use subtraction and division properties of inequality. Subtract 4 from both the sides then divide each side by 3 and simplify.

$\begin{array}{c}3x+4-4\ge 19-4\\ \frac{3x}{3}\ge \frac{15}{3}\\ x\ge 5\end{array}$

Thus, solution is $x\ge 5$.

– Describe solution set in interval notation.

Assolution set of the inequality is all real numbers greater than or equal to 5.

Write the solution set in interval notation.

$[5,+\infty )$

– Graph the solution set.

Closed circle on 5 shows this point is included in the solution set.