Question

solve the inequality and graph the solution.
2z + 2 < 10
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
submit

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( z \), we subtract 2 from both sides of the inequality \( 2z + 2 < 10 \). This gives us \( 2z + 2 - 2 < 10 - 2 \), which simplifies to \( 2z < 8 \).

Step2: Divide both sides by 2

To solve for \( z \), we divide both sides of the inequality \( 2z < 8 \) by 2. This gives us \( \frac{2z}{2} < \frac{8}{2} \), which simplifies to \( z < 4 \).

Answer:

The solution to the inequality \( 2z + 2 < 10 \) is \( z < 4 \). To graph this, we draw an open circle at \( z = 4 \) (since the inequality is strict, \( z \) cannot equal 4) and shade the line to the left of 4 to represent all values of \( z \) less than 4.