Chapter A, Problem 11E

To determine

To solve: The inequality in terms of intervals and illustrate the solution set on real time line.

Answer to Problem 11E

The value for the given expression is   $x\in \left(-2,\infty \right)$.

Explanation of Solution

Given:

The expression is $2x+7>3$.

Calculation:

The expression can be re written as,

$\begin{array}{l}2x+7>3\\ 2x>3-7\\ 2x>-4\\ x>\frac{-4}{2}\end{array}$

$x>-2$

Therefore, $x\in \left(-2,\infty \right)$.

Thus, the equivalent form of the inequality in the interval notation is $x\in \left(-2,\infty \right)$.

The interval $\left(-2,\infty \right)$ is shown below in Figure 1

From Figure 1, it is observed that the value of x belongs to the darkened region in the number line.