Question

use substitution to check your solutions. b. 17 = a - 8 c. 9 + b = 15

Explanation:

Part b: Solving \( 17 = a - 8 \)

Step 1: Isolate \( a \)

To solve for \( a \), we add 8 to both sides of the equation.
\( 17 + 8 = a - 8 + 8 \)

Step 2: Simplify both sides

Simplifying the left side: \( 17 + 8 = 25 \). Simplifying the right side: \( a - 8 + 8 = a \). So we get \( a = 25 \).

Step 3: Check the solution (substitution)

Substitute \( a = 25 \) back into the original equation \( 17 = a - 8 \).
Left side: \( 17 \)
Right side: \( 25 - 8 = 17 \)
Since left side = right side, the solution is correct.

Part c: Solving \( 9 + b = 15 \)

Step 1: Isolate \( b \)

To solve for \( b \), we subtract 9 from both sides of the equation.
\( 9 + b - 9 = 15 - 9 \)

Step 2: Simplify both sides

Simplifying the left side: \( 9 + b - 9 = b \). Simplifying the right side: \( 15 - 9 = 6 \). So we get \( b = 6 \).

Step 3: Check the solution (substitution)

Substitute \( b = 6 \) back into the original equation \( 9 + b = 15 \).
Left side: \( 9 + 6 = 15 \)
Right side: \( 15 \)
Since left side = right side, the solution is correct.

Answer:

• For part b: \( a = 25 \)
• For part c: \( b = 6 \)