Question

9 solve the inequality $\frac{x}{5} - 4 > -3$ for $x$. show your work. then graph the solution set.

Explanation:

Step1: Add 4 to both sides

To isolate the term with \( x \), we add 4 to both sides of the inequality \(\frac{x}{5}-4 > -3\). This gives us \(\frac{x}{5}-4 + 4> -3 + 4\), which simplifies to \(\frac{x}{5}>1\).

Step2: Multiply both sides by 5

To solve for \( x \), we multiply both sides of the inequality \(\frac{x}{5}>1\) by 5. This gives us \(5\times\frac{x}{5}>1\times5\), which simplifies to \(x > 5\).

Answer:

The solution to the inequality \(\frac{x}{5}-4 > -3\) is \(x > 5\). To graph the solution set, we draw a number line, place an open circle at 5 (since \( x \) is not equal to 5), and shade the region to the right of 5 to represent all values of \( x \) greater than 5.