Question

1. 81 + 68x = 1,849
2. 57z + 93 = 435
3. 77 + 82x = 7,867

Explanation:

Problem 8: \( 81 + 68x = 1849 \)

Step 1: Subtract 81 from both sides

To isolate the term with \( x \), we subtract 81 from both sides of the equation.
\( 81 + 68x - 81 = 1849 - 81 \)
Simplifying both sides, we get:
\( 68x = 1768 \)

Step 2: Divide both sides by 68

To solve for \( x \), we divide both sides of the equation by 68.
\( x = \frac{1768}{68} \)
Simplifying the right - hand side, we find that \( \frac{1768}{68}=26 \)

Step 1: Subtract 93 from both sides

To isolate the term with \( z \), we subtract 93 from both sides of the equation.
\( 57z + 93-93=435 - 93 \)
Simplifying both sides, we get:
\( 57z=342 \)

Step 2: Divide both sides by 57

To solve for \( z \), we divide both sides of the equation by 57.
\( z=\frac{342}{57} \)
Simplifying the right - hand side, we find that \( \frac{342}{57} = 6 \)

Step 1: Subtract 77 from both sides

To isolate the term with \( x \), we subtract 77 from both sides of the equation.
\( 77 + 82x-77=7867 - 77 \)
Simplifying both sides, we get:
\( 82x=7790 \)

Step 2: Divide both sides by 82

To solve for \( x \), we divide both sides of the equation by 82.
\( x=\frac{7790}{82} \)
Simplifying the right - hand side, we find that \( \frac{7790}{82}=95 \)

Answer:

\( x = 26 \)

Problem 10: \( 57z+93 = 435 \)