Question

solve the inequality and graph the solution on the line provided.
-6x + 2 > 32
answer attempt 1 out of 2
inequality notation:
number line:

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( z \), we subtract 2 from both sides of the inequality \(-6z + 2>32\).

$$ -6z + 2-2>32 - 2 $$

Simplifying both sides, we get:

$$ -6z>30 $$

Step2: Divide by -6 (reverse inequality)

When dividing an inequality by a negative number, we reverse the inequality sign. We divide both sides of \(-6z>30\) by \(-6\).

$$ \frac{-6z}{-6}<\frac{30}{-6} $$

Simplifying both sides, we find:

$$ z < - 5 $$

Answer:

Inequality Notation: \(z < -5\)

For the number line: Draw an open circle at \(-5\) (since \(z\) is not equal to \(-5\)) and shade the line to the left of \(-5\) to represent all values of \(z\) less than \(-5\).