Question

Solve the inequality $\left|x-4\right|\mathbf{<}\mathbf{0}\mathbf{.}\mathbf{02}$, express the solution using interval notation and graph the solution set on real number line.

Short answer

The solution of the inequality $\left|x-4\right|<0.02$is$3.98<x<4.02$ whose interval notation is $x\in \left(3.98,4.02\right)$and graph is shown on real number line.

Step-by-step solution

Step 1. Solve the given inequality.

$\begin{array}{c}\left|x-4\right|<\mathrm{0.02....}\left(\text{Given}\right)\\ -0.02>x-4<0.02\\ x-4>-0.02\text{and}x-4<0.02\\ x>3.98\text{and}x<4.02\end{array}$

Combining both solutions $x>3.98\text{and}x<4.02$, the solution of the inequality is $3.98<x<4.02$.

Step 2. Writing interval notation and graph of solution on real number line.

The interval notation for$3.98<x<4.02$ is written as$x\in \left(3.98,4.02\right)$.

The graph of solution on real number line is shown below.

Step 3. DESCRIPTION OF STEPS.

The solution of the inequality is$3.98<x<4.02$ whose interval notation is $x\in \left(3.98,4.02\right)$.