Which value of x would make line segment t v is parallel to line segment q s? 3 8 10 11

The value of x that would make the line segment TV to be parallel to the line segment QS is;

Option C; 10

The image of the line segment is missing and so i have attached it.

    From the attached image of the triangle, we can use the theorem of similar triangles to get;

RT/RQ = RV/RS

We see that;

RT = x + 4

RQ = x + 4 + x - 3 = 2x + 1

RV = x + 10

RS = x + 10 + x = 2x + 10

Thus;

(x + 4)/(2x + 1) = (x + 10)/(2x + 10)

Cross multiply to get;

(x + 4)(2x + 10) = (x + 10)(2x + 1)

2x² + 18x + 40 = 2x² + 21x + 10

2x² will cancel out to give;

18x + 40 = 21x + 10

21x - 18x = 40 - 10

3x = 30

x = 30/3

x = 10

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is means division by fractions

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