Question

solve the inequality and graph the solution. 8 + 9u > -10 to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it. -5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( u \), we subtract 8 from both sides of the inequality \( 8 + 9u > -10 \). This gives us \( 8 + 9u - 8 > -10 - 8 \), which simplifies to \( 9u > -18 \).

Step2: Divide by 9

Next, we divide both sides of the inequality \( 9u > -18 \) by 9 to solve for \( u \). So, \( \frac{9u}{9} > \frac{-18}{9} \), which simplifies to \( u > -2 \).

For graphing the solution:

• The endpoint is at \( -2 \). Since the inequality is \( u > -2 \) (not \( u \geq -2 \)), the endpoint is an open circle.
• The arrow points to the right (towards positive infinity) because we want all values of \( u \) greater than \( -2 \).

Answer:

The solution to the inequality is \( u > -2 \). For the graph, plot an open circle at \( -2 \) and draw an arrow pointing to the right.