Question

sv is the midsegment of the trapezoid tuwx. if tu = -2z + 14, sv = 3z - 3, and wx = z + 8, what is the value of z?

Explanation:

Step1: Recall mid - segment formula

The formula for the mid - segment of a trapezoid is $SV=\frac{TU + WX}{2}$.

Step2: Substitute given expressions

Substitute $TU=-2z + 14$, $SV = 3z-3$, and $WX=z + 8$ into the formula: $3z-3=\frac{-2z + 14+z + 8}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator of the right - hand side: $-2z+14 + z + 8=-z + 22$. So the equation becomes $3z-3=\frac{-z + 22}{2}$.

Step4: Cross - multiply

Multiply both sides of the equation by 2 to get rid of the fraction: $2(3z-3)=-z + 22$.

Step5: Expand the left - hand side

Use the distributive property: $6z-6=-z + 22$.

Step6: Add z to both sides

$6z+z-6=-z+z + 22$, which simplifies to $7z-6 = 22$.

Step7: Add 6 to both sides

$7z-6+6=22 + 6$, so $7z=28$.

Step8: Solve for z

Divide both sides by 7: $z=\frac{28}{7}=4$.

Answer:

$4$