Question

PQ || MN || SR and PM = MS. Find x if QN = 3x + 1 and NR = 2x + 6.

Options

• 1

• 5

• 3

• 2

Answer 1

5

Explanation:

Step 1:

Set up the proportion

• Since PQ || MN || SR, we have the proportion `(PM)/(MS) = (QN)/(NR)`
• Given that PM = MS, we have `(PM)/(MS)` = 1
• Therefore, `(QN)/(NR)` = 1.

Step 2:

Substitute the given values

• Substitute the given expressions for QN and NR into the proportion: `(3x + 1)/(2x + 6) = 1`

Step 3:

Solve for x

• Multiply both sides by 2x + 6: 3x + 1 = 2x + 6
• Subtract 2x from both sides: x + 1 = 6
• Subtract 1 from both sides: x = 5