Questions: PT=4x+5 and TQ=6x-9

PT=4x+5 and TQ=6x-9
Transcript text: PT=4x+5 and TQ=6x-9
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Solution

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Solution Steps

To solve for \( x \) given the equations for PT and TQ, we need to set up an equation that relates PT and TQ. If PT and TQ are parts of a line segment PQ, we can set up an equation based on the given expressions and solve for \( x \).

Step 1: Define the Equations

We are given the equations for \( \mathrm{PT} \) and \( \mathrm{TQ} \): \[ \mathrm{PT} = 4x + 5 \] \[ \mathrm{TQ} = 6x - 9 \]

Step 2: Set Up the Equation

To find \( x \), we set the expressions for \( \mathrm{PT} \) and \( \mathrm{TQ} \) equal to each other: \[ 4x + 5 = 6x - 9 \]

Step 3: Solve for \( x \)

Rearrange the equation to isolate \( x \): \[ 4x + 5 = 6x - 9 \] \[ 5 + 9 = 6x - 4x \] \[ 14 = 2x \] \[ x = 7 \]

Final Answer

\(\boxed{x = 7}\)

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