Question

1. solve the inequality and graph its solution.

80 > 10x

Explanation:

Step1: Isolate the variable x

To solve the inequality \( 80 > 10x \), we divide both sides of the inequality by 10. When dividing both sides of an inequality by a positive number, the direction of the inequality sign remains the same. So we have:
\( \frac{80}{10} > \frac{10x}{10} \)

Step2: Simplify both sides

Simplifying the left side, \( \frac{80}{10}=8 \), and simplifying the right side, \( \frac{10x}{10} = x \). So the inequality simplifies to:
\( 8 > x \) or equivalently \( x < 8 \)

To graph the solution: On a number line, we draw an open circle at 8 (since the inequality is strict, \( x
eq8 \)) and shade the region to the left of 8 to represent all values of \( x \) that are less than 8.

Answer:

The solution to the inequality \( 80 > 10x \) is \( x < 8 \). The graph has an open circle at 8 and shading to the left of 8 on the number line.