Q31. - Algebra 2

Question

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

$6d+3\ge 5d-2$

Step-by-Step Solution

Answer

Solution of inequality $6d+3\ge 5d-2$ is $d\ge -5$

In interval form, solution set is $\left[-5,\infty \right)$

Solution set on number line is 

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify 6 d + 3 ≥ 5 d − 2

To simplify given inequality, use subtraction property of inequalities. Subtract same numbers from both sides does not change the sign of inequality as shown below

$\begin{array}{c}6d+3\ge 5d-2\\ 6d-5d+3-3\ge 5d-5d-2-3\\ d\ge -5\end{array}$

Step 3 - Write solution set

The solution set of the inequality contains all real numbers greater than or equal to $-5$

As, $-5$ is included in the set so bracket is used with it also $\infty$ is not included so parentheses is used with it.

In interval form solution set is $\left[-5,\infty \right)$

Step 4 - Graph the solution set

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

So arrow is towards $\infty$ and dot on $-5$ shows it is included in the solution set.