Question

solve and graph each inequality

1. x - 13 ≤ 5

Explanation:

Step1: Add 13 to both sides

To solve the inequality \( x - 13 \leq 5 \), we add 13 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the inequality sign remains the same.

So, \( x - 13 + 13 \leq 5 + 13 \)

Step2: Simplify both sides

Simplifying the left - hand side: \( x-13 + 13=x\)

Simplifying the right - hand side: \(5 + 13 = 18\)

So we get \(x\leq18\)

For graphing the inequality \(x\leq18\) on a number line:

1. Draw a number line.
2. Locate the number 18 on the number line.
3. Since the inequality is \(x\leq18\) (less than or equal to), we use a closed circle (a filled - in dot) at 18 to indicate that 18 is included in the solution set.
4. Then, we draw an arrow to the left of 18 to show that all numbers less than 18 are also part of the solution set.

Answer:

The solution to the inequality \(x - 13\leq5\) is \(x\leq18\). The graph has a closed circle at 18 and an arrow pointing to the left.