Q. 26 - Algebra 2

Question

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

 $\mathbf{3}\mathbf{q}\mathbf{+}\mathbf{7}\ge \mathbf{13}$

Step-by-Step Solution

Answer

Solution set of inequality is $\mathbf{[}\mathbf{2}\mathbf{,}\mathbf{+}\infty \mathbf{)}$.

Solution set on number line is 

Step 1. Write properties of inequality.

Properties of inequalities are written in following table:

Step 2. Solve 3 q + 7 ≥ 13 .

To solve given inequality, use subtraction and division properties of inequality. Subtract 7 from each side and do not change the sign of inequality then divide each side by 3 and simplify.

$\begin{array}{c}3q+7-7\ge 13-7\\ \frac{3q}{3}\ge \frac{6}{3}\\ q\ge 2\end{array}$

Thus, solution is $q\ge 2$.

Step 3. Describe solution set in interval notation.

As solution set of the inequality is all real numbers greater than or equal to 2.

Write the solution set in interval notation.

$[2,+\infty )$

Step 4. Graph the solution set.

Closed circle on 2 shows this point is included in the solution set.