Chapter 8.8, Problem 67CCR

To determine

Solve the inequality $-\frac{3}{4}<w-1$ and graph the solution on number line

Answer to Problem 67CCR

The solution of the inequality is $w>\frac{1}{4}$

The graph of the solution $w>\frac{1}{4}$ on number line is below:

  

Explanation of Solution

Given:

The inequality, $-\frac{3}{4}<w-1$

Concept used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

• In order to solve the mixed inequality $-\frac{3}{4}<w-1$ first isolate the variable term w by performing some basic operations. Here to isolate w terms on the left side, first add both sides by $1$ and then simplify further as shown below:

  $\begin{array}{c}-\frac{3}{4}<w-1\\ -\frac{3}{4}+1<w-1+1\\ -\frac{3+4}{4}<w\\ \frac{1}{4}<w\\ \Rightarrow w>\frac{1}{4}\end{array}$

Thus, the solution of the given inequality is $w>\frac{1}{4}$ .

The graph of the inequality solution $w>\frac{1}{4}$ is below: