Answer:

[tex]PQ = 42[/tex]

Step-by-step explanation:

Given

[tex]PT = 3x + 3[/tex]

[tex]TQ = 5x – 9[/tex]

Midpoint, T

Required

Determine PT

First, the value of x has to be calculated;

Since T is the midpoint, then:

[tex]PT = TQ[/tex]

This implies

[tex]3x + 3 = 5x – 9[/tex]

Solve for x

[tex]3x – 5x = -3 – 9[/tex]

[tex]-2x = -12[/tex]

[tex]x = -12/-2[/tex]

[tex]x = 6[/tex]

Length PQ can then be calculated using:

[tex]PQ = PT + TQ[/tex]

[tex]PQ = 3x +3 + 5x -9[/tex]

Collect Like Terms

[tex]PQ = 3x+ 5x +3 -9[/tex]

[tex]PQ = 8x -6[/tex]

Substitute 6 for x

[tex]PQ = 8 * 6 – 6[/tex]

[tex]PQ = 48 – 6[/tex]

[tex]PQ = 42[/tex]

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