Question

7 solve the inequality and graph the solution. 10x - 15 > -5

Explanation:

Step1: Add 15 to both sides

To isolate the term with \( x \), we add 15 to both sides of the inequality \( 10x - 15 > -5 \). This gives us \( 10x - 15 + 15 > -5 + 15 \), which simplifies to \( 10x > 10 \).

Step2: Divide both sides by 10

To solve for \( x \), we divide both sides of the inequality \( 10x > 10 \) by 10. This gives us \( \frac{10x}{10} > \frac{10}{10} \), which simplifies to \( x > 1 \).

For graphing the solution: On a number line, we draw an open circle at \( x = 1 \) (since the inequality is \( > \), not \( \geq \)) and shade the region to the right of 1 to represent all values of \( x \) greater than 1.

Answer:

The solution to the inequality \( 10x - 15 > -5 \) is \( x > 1 \). The graph has an open circle at \( 1 \) and shading to the right.