Question

1. rq = 3x + 8

qs = 2x − 5
rs = 43

rq =____ qs =____

Explanation:

Step1: Set up the equation

Since \( RQ + QS = RS \), substitute the given expressions: \( (3x + 8) + (2x - 5) = 43 \).
Simplify the left side: \( 3x + 8 + 2x - 5 = 5x + 3 \). So, \( 5x + 3 = 43 \).

Step2: Solve for \( x \)

Subtract 3 from both sides: \( 5x = 43 - 3 = 40 \).
Divide both sides by 5: \( x = \frac{40}{5} = 8 \).

Step3: Find \( RQ \)

Substitute \( x = 8 \) into \( RQ = 3x + 8 \): \( RQ = 3(8) + 8 = 24 + 8 = 32 \).

Step4: Find \( QS \)

Substitute \( x = 8 \) into \( QS = 2x - 5 \): \( QS = 2(8) - 5 = 16 - 5 = 11 \).

Answer:

\( RQ = 32 \), \( QS = 11 \)