Question

solve the inequality and graph the solution. 76 < 19q plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it. submit

Explanation:

Step1: Isolate the variable \( q \)

To solve the inequality \( 76 < 19q \), we divide both sides by 19.

$$ \frac{76}{19} < \frac{19q}{19} $$

Step2: Simplify both sides

Simplifying the left side, \( \frac{76}{19} = 4 \), and the right side simplifies to \( q \). So we get \( 4 < q \), or equivalently \( q > 4 \).
For graphing, since the inequality is \( q > 4 \), the endpoint at 4 is open (because 4 is not included in the solution), and we draw a ray to the right of 4 on the number line.

Answer:

The solution to the inequality \( 76 < 19q \) is \( q > 4 \). For the graph, place an open circle at 4 and draw a line (ray) extending to the right from 4.