Question

olve the inequality and graph the solution on the line ovided.
$-5x + 24 geq -1$

1. solve for $z$.

$26 - 5z = -49$

1. solve for $z$.

$\frac{1}{3}z + 23 = 32$

1. solve for $y$. express your answer as a proper or improper fraction in simplest terms.

$-\frac{1}{8} - \frac{1}{3}y = -\frac{1}{2}$

1. solve the following equation for $a$.

$\frac{n}{r} = \frac{b}{a}$

1. solve the following equation for $a$.

$g = -m + \frac{1}{8}a$

1. solve the following equation for $y$.

$j = -q + y$

Explanation:

Problem 24: Solve for \( z \) in \( 26 - 5z = -49 \)

Step 1: Subtract 26 from both sides

To isolate the term with \( z \), we subtract 26 from both sides of the equation.
\( 26 - 5z - 26 = -49 - 26 \)
Simplifying both sides gives:
\( -5z = -75 \)

Step 2: Divide both sides by -5

To solve for \( z \), we divide both sides of the equation by -5.
\( \frac{-5z}{-5} = \frac{-75}{-5} \)
Simplifying both sides gives:
\( z = 15 \)

Step 1: Subtract 23 from both sides

To isolate the term with \( z \), we subtract 23 from both sides of the equation.
\( \frac{1}{3}z + 23 - 23 = 32 - 23 \)
Simplifying both sides gives:
\( \frac{1}{3}z = 9 \)

Step 2: Multiply both sides by 3

To solve for \( z \), we multiply both sides of the equation by 3.
\( 3 \times \frac{1}{3}z = 9 \times 3 \)
Simplifying both sides gives:
\( z = 27 \)

Step 1: Add \( \frac{1}{8} \) to both sides

To isolate the term with \( y \), we add \( \frac{1}{8} \) to both sides of the equation.
\( -\frac{1}{8} - \frac{1}{3}y + \frac{1}{8} = -\frac{1}{2} + \frac{1}{8} \)
Simplifying both sides gives:
\( -\frac{1}{3}y = -\frac{4}{8} + \frac{1}{8} \)
\( -\frac{1}{3}y = -\frac{3}{8} \)

Step 2: Multiply both sides by -3

To solve for \( y \), we multiply both sides of the equation by -3.
\( -3 \times (-\frac{1}{3}y) = -\frac{3}{8} \times (-3) \)
Simplifying both sides gives:
\( y = \frac{9}{8} \)

Answer:

\( z = 15 \)

Problem 25: Solve for \( z \) in \( \frac{1}{3}z + 23 = 32 \)