Question

Solve the inequality. Graph your solution.

$\mathbf{3}\mathbf{y}\mathbf{-}\mathbf{5}\mathbf{<}\mathbf{2}\mathbf{(}\mathbf{17}\mathbf{-}\mathbf{5}\mathbf{y}\mathbf{)}$

Short answer

Solution of the inequality is $y<3$.

Step-by-step solution

Step 1. Solve the inequality

$3y-5<2(17-5y)$

Use the distributive property.

$3y-5<34-10y$

Add 5 and 10y on both the sides.

$\begin{array}{c}3y-5+5+10y<34-10y+10y+5\\ 13y<39\end{array}$

Divide both sides by 13.

$\begin{array}{c}y<\frac{39}{13}\\ y<3\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $y<3$.

That means, all values $y<3$ 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, $y<3$ and substitute in the original inequality and observe the result.

Take $b=0$.

Then,

$\begin{array}{c}3\times 0-5<2(17-5\times 0)\\ 0-5<2\left(17-0\right)\\ -5<34\end{array}$

The result $-5<34$ is true. So, the solution $y<3$ is correct.