Question

graph the solution set. 4. \\(\frac{x}{3} - 5 \leq -6\\)

Explanation:

Step1: Add 5 to both sides

To isolate the term with \( x \), we add 5 to both sides of the inequality \(\frac{x}{3}-5 \leq -6\). This gives us \(\frac{x}{3}-5 + 5\leq -6 + 5\), which simplifies to \(\frac{x}{3}\leq -1\).

Step2: Multiply both sides by 3

To solve for \( x \), we multiply both sides of the inequality \(\frac{x}{3}\leq -1\) by 3. This gives us \(3\times\frac{x}{3}\leq 3\times(-1)\), which simplifies to \(x\leq - 3\).

Answer:

The solution to the inequality \(\frac{x}{3}-5 \leq -6\) is \(x\leq - 3\). To graph this, we draw a closed circle at \(-3\) on the number line and shade to the left of \(-3\) (since \(x\) is less than or equal to \(-3\)).