Questions: x= P Q=0

x= P Q=0
Transcript text: x= \[ P Q=0 \]
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given a line segment PQ with point R between P and Q. The lengths PR and RQ are expressed as algebraic expressions in terms of x. We need to find the value of x and then use it to find the length of PQ.

Step 2: Set Up the Equation

Since R is between P and Q, the sum of PR and RQ should equal PQ. Therefore, we can write the equation: \[ PR + RQ = PQ \] Given: \[ PR = 15x - 2 \] \[ RQ = 5x + 3 \] \[ PQ = PR + RQ \]

Step 3: Substitute and Solve for x

Substitute the given expressions into the equation: \[ 15x - 2 + 5x + 3 = PQ \] Combine like terms: \[ 20x + 1 = PQ \]

Step 4: Use the Given Value of x

We are given that \( x = 0.5 \). Substitute this value into the equation: \[ 20(0.5) + 1 = PQ \] \[ 10 + 1 = PQ \]

Final Answer

\[ PQ = 11 \]

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