Question

question 38 (3 points)
solve the inequality. give the solution set in both interval and graph forms.
30x - 15 > 5(5x - 5)
options:
(-∞, 30) with corresponding number line graph
(30, ∞) with corresponding number line graph
(-2, ∞) with corresponding number line graph
(-∞, -2) with corresponding number line graph

Explanation:

Step1: Expand the right side

Expand \(5(5x - 5)\) to get \(25x - 25\). So the inequality becomes \(30x - 15 > 25x - 25\).

Step2: Subtract \(25x\) from both sides

Subtract \(25x\) from each side: \(30x - 25x - 15 > 25x - 25x - 25\), which simplifies to \(5x - 15 > -25\).

Step3: Add 15 to both sides

Add 15 to each side: \(5x - 15 + 15 > -25 + 15\), resulting in \(5x > -10\).

Step4: Divide by 5

Divide both sides by 5: \(\frac{5x}{5} > \frac{-10}{5}\), so \(x > -2\).

The interval notation for \(x > -2\) is \((-2, \infty)\), and the graph should have an open circle at \(-2\) and an arrow pointing to the right (matching the third option's graph).

Answer:

\((-2, \infty)\) (with the corresponding graph: the number line with an open circle at \(-2\) and arrow to the right, as in the third option)