Question

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

$a+2<3.5$

Short answer

Solution of inequality $a+2<3.5$ is $a<1.5$

In interval notation solution set is $\left(-\infty ,1.5\right)$

Solution set on line is

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify a+2<3.5

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

$\begin{array}{c}a+2<3.5\\ a+2-2<3.5-2\\ a<1.5\end{array}$

- Write solution set

The solution set of the inequality $a<1.5$ contains all real number less than $1.5$

In interval notation, solution set contains all real number between $-\infty$ to $1.5$ and both the end points are not included so parentheses is used to denote interval.

Solution set is $\left(-\infty ,1.5\right)$

- Graph the solution set

Assolution set of the inequality $a<1.5$ contains all real number less than $1.5$

So arrow is towards $-\infty$ and open circle on $1.5$ denotes it is not included in the solution set.