Question

what value of z is a solution to this equation?
$-19 = -\frac{z}{2} - 13$
$z = -10$ $z = 12$

Explanation:

Step1: Add 13 to both sides

To isolate the term with \( z \), we add 13 to both sides of the equation \( -19 = -\frac{z}{2}-13 \).

$$ -19 + 13=-\frac{z}{2}-13 + 13 $$

Simplifying both sides, we get:

$$ -6 = -\frac{z}{2} $$

Step2: Multiply both sides by -2

To solve for \( z \), we multiply both sides of the equation \( -6 = -\frac{z}{2} \) by -2.

$$ -6\times(-2)=-\frac{z}{2}\times(-2) $$

Simplifying both sides, we find:

$$ 12 = z $$

We can also check by substituting the given values. For \( z = - 10\):
Left - hand side of the equation: \( -19\)
Right - hand side: \( -\frac{-10}{2}-13=5 - 13=-8
eq - 19\)
For \( z = 12\):
Right - hand side: \( -\frac{12}{2}-13=-6 - 13=-19\), which is equal to the left - hand side.

Answer:

\( z = 12 \)