Question

solve the inequality. graph the solution.

1. ( x - 4 < 8 )

Explanation:

Step1: Add 4 to both sides

To isolate \( x \), we add 4 to both sides of the inequality \( x - 4 < 8 \). This gives us \( x - 4 + 4 < 8 + 4 \).

Step2: Simplify both sides

Simplifying the left side, \( x - 4 + 4 \) becomes \( x \). Simplifying the right side, \( 8 + 4 \) is \( 12 \). So the solution to the inequality is \( x < 12 \).

For graphing the solution: On a number line, we draw an open circle at 12 (since \( x \) is not equal to 12) and shade the region to the left of 12 to represent all values of \( x \) that are less than 12.

Answer:

The solution to the inequality \( x - 4 < 8 \) is \( x < 12 \). The graph has an open circle at 12 and shading to the left.