Question

Solve the inequality. Graph your solution.

$\mathbf{4}\left(\mathbf{5}\mathbf{-}\mathbf{3}\mathbf{b}\right)\mathbf{>}\mathbf{4}\mathbf{b}\mathbf{+}\mathbf{4}$

Short answer

Solution of the inequality is $b<1$.

Step-by-step solution

Step 1. Solve the inequality

$4\left(5-3b\right)>4b+4$

Use the distributive property.

$20-12b>4b+4$

Subtract 20 and 4b on both the sides.

$\begin{array}{c}20-12b-20-4b>4b+4-4b-20\\ -16b>-16\end{array}$

Divide both sides by -16.

$\begin{array}{c}b<\frac{-16}{-16}\\ b<1\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $b<1$.

That means, all values $b<1$ 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, $b<1$ and substitute in the original inequality and observe the result.

Take $b=0$.

Then,

$\begin{array}{c}4\left(5-3\times 0\right)>4\times 0+4\\ 4\left(5-0\right)>0+4\\ 4\times 5>4\\ 20>4\end{array}$

The result $20>4$ is true. So, the solution $b<1$ is correct.