Question

solve each inequality and graph its

1. $\frac{x}{14} + 3 \geq 4$

number line from 11 to 21

Explanation:

Step1: Subtract 3 from both sides

To isolate the term with \( x \), we subtract 3 from both sides of the inequality \(\frac{x}{14}+3\geq4\). This gives us \(\frac{x}{14}+3 - 3\geq4 - 3\), which simplifies to \(\frac{x}{14}\geq1\).

Step2: Multiply both sides by 14

To solve for \( x \), we multiply both sides of the inequality \(\frac{x}{14}\geq1\) by 14. This gives us \(\frac{x}{14}\times14\geq1\times14\), which simplifies to \(x\geq14\).

Answer:

The solution to the inequality \(\frac{x}{14}+3\geq4\) is \(x\geq14\). To graph this, we would shade the number line from 14 (including 14, so we use a closed dot at 14) to the right.