Question

Solve the inequality. Graph your solution.

$\frac{x}{-4}\le -6$

Short answer

$\mathbf{x}\ge \mathbf{24}$

Step-by-step solution

Step 1. Given information

Inequality: $\frac{x}{-4}\le -6$

Step 2. Calculation 

Consider given inequality $\frac{x}{-4}\le -6$,

$\begin{array}{l}\frac{x}{-4}\le -6\\ \frac{x}{-4}\times -4\ge -6\times -4\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Multiplying-4onbothsidesandreversetheinequalitysymbol]}\\ x\ge 24\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}[}\because \text{Simplify]}\end{array}$

Step 3. Graph 

Using graphing calculator to draw the above inequality,

Step 4. Interpretation

The above graph represents the inequality $x\ge 24$.

Therefore, $x\ge 24$ is the required solution.