Question

solve the inequality and graph the solution.
7 - b < 9
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 7 from both sides

To isolate the term with \( b \), we subtract 7 from both sides of the inequality \( 7 - b < 9 \). This gives us \( 7 - b - 7 < 9 - 7 \), which simplifies to \( -b < 2 \).

Step2: Multiply by -1 (reverse inequality)

When we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign. Multiplying both sides of \( -b < 2 \) by -1 gives \( b > -2 \).

Answer:

The solution to the inequality \( 7 - b < 9 \) is \( b > -2 \). To graph this, we draw an open circle at \( -2 \) (since the inequality is strict, \( b
eq -2 \)) and shade the line to the right of \( -2 \).