Question

Solve the inequality. Graph your solution.

$\mathbf{3}\mathbf{+}\frac{\mathbf{b}}{\mathbf{3}}\mathbf{<}\mathbf{7}$

Short answer

Solution of the inequality is $b<12$.

Step-by-step solution

Step 1. Solve the inequality

$3+\frac{b}{3}<7$

Subtract 3 from both the sides.

$\begin{array}{c}3-3+\frac{b}{3}<7-3\\ \frac{b}{3}<4\end{array}$

Multiply both sides by 3.

$\begin{array}{c}\frac{b}{3}\times 3<4\times 3\\ b<12\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $b<12$.

That means, all values $b<12$ satisfy the inequality. So, the graph can be given as shown below.

Step 3. Check the solution

To check the solution, take any random number, $b<12$ and substitute in the original inequality and observe the result.

Take $b=0$.

Then,

$\begin{array}{c}3+\frac{0}{3}<7\\ 3+0<7\\ 3<7\end{array}$

The result $3<7$ is true. So, the solution $b<12$ is correct.