Question

Solve the inequality. Graph your solution.

$\mathbf{6}\mathbf{n}\mathbf{-}\mathbf{3}\le \mathbf{-}\mathbf{9}$

Short answer

Solution of the inequality is $n\le -1$.

Step-by-step solution

Step 1. Solve the inequality

$6n-3\le -9$

Add 3 both the sides.

$\begin{array}{c}6n-3+3\le -9+3\\ 6n\le -6\end{array}$

Divide both sides by 6.

$\begin{array}{c}n\le \frac{-6}{6}\\ n\le -1\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $n\le -1$.

That means, all values $n\le -1$ 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, $n\le -1$ and substitute in the original inequality and observe the result.

Take $n=-2$.

Then,

$\begin{array}{c}6\left(-2\right)-3\le -9\\ -12-3\le -9\\ -15\le -9\end{array}$

The result $-15\le -9$ is true. So, the solution $n\le -1$ is correct.