Q4. - Algebra 2

Question

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

$a+2<3.5$

Step-by-Step Solution

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 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify a + 2 &#60; 3.5

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

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

Step 3 - 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 $\left(-\infty ,1.5\right)$

Step 4 - Graph the solution set

As solution 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.