Question

solve the inequality and graph the solution on the line provided.
-18 + 3x > 6

Explanation:

Step1: Add 18 to both sides

To isolate the term with \( x \), we add 18 to both sides of the inequality \( -18 + 3x > 6 \). This gives us \( -18 + 18 + 3x > 6 + 18 \), which simplifies to \( 3x > 24 \).

Step2: Divide by 3

Next, we divide both sides of the inequality \( 3x > 24 \) by 3 to solve for \( x \). So, \( \frac{3x}{3} > \frac{24}{3} \), which simplifies to \( x > 8 \).

For graphing the solution on a number line: We draw an open circle at 8 (since the inequality is \( > \), not \( \geq \)) and shade the region to the right of 8 to represent all values of \( x \) that are greater than 8.

Answer:

The solution to the inequality is \( x > 8 \). For the graph, there is an open circle at 8 and shading to the right of 8 on the number line.