Q61. - 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.

$\mathbf{2}\mathbf{d}\mathbf{+}\mathbf{15}\ge \mathbf{3}$

 

Step-by-Step Solution

Answer

Solution set of inequality is $\mathbf{[}\mathbf{-}\mathbf{6}\mathbf{,}\mathbf{+}\infty \mathbf{)}$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve 2 d + 15 ≥ 3 .

To solve given inequality, use subtraction and division properties of inequality. Subtract 15 from each side and do not change the sign of inequality. Then divide by 2 on each side and simplify.

$\begin{array}{l}2d+15-15\ge 3-15\\ \frac{2d}{2}\ge -\frac{12}{2}\\ d\ge -6\end{array}$

 Thus, solution is $d\ge -6$.

Step 3 – Describe solution set in interval notation.

As solution set of the inequality is all real numbers greater than or equal to $-6$.

Write the solution set in interval notation.

$[-6,+\infty )$

Step 4 – Graph the solution set.

Number line starts from $-6$ to $\infty$.

Dot on $-6$ shows this point is included in the solution set