Question

1. 17=3(x−5)+8
2. 18=−2(x−5)+4x

Explanation:

Problem 14: \( 17 = 3(x - 5) + 8 \)

Step 1: Simplify the right side

First, distribute the 3 in \( 3(x - 5) \): \( 3x - 15 \). Then the equation becomes \( 17 = 3x - 15 + 8 \). Combine like terms: \( -15 + 8 = -7 \), so \( 17 = 3x - 7 \).

Step 2: Solve for \( x \)

Add 7 to both sides: \( 17 + 7 = 3x \), which simplifies to \( 24 = 3x \). Divide both sides by 3: \( x = \frac{24}{3} = 8 \).

Step 1: Simplify the right side

Distribute the -2 in \( -2(x - 5) \): \( -2x + 10 \). Then the equation becomes \( 18 = -2x + 10 + 4x \). Combine like terms: \( -2x + 4x = 2x \), so \( 18 = 2x + 10 \).

Step 2: Solve for \( x \)

Subtract 10 from both sides: \( 18 - 10 = 2x \), which simplifies to \( 8 = 2x \). Divide both sides by 2: \( x = \frac{8}{2} = 4 \).

Answer:

\( x = 8 \)

Problem 17: \( 18 = -2(x - 5) + 4x \)