Q41. - 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.

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

Step-by-Step Solution

Answer

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

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve 3 x + 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 $x\ge 5$.

Step 3 – Describe solution set in interval notation.

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

Write the solution set in interval notation.

$[5,+\infty )$

Step 4 – Graph the solution set.

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