Question

48/55 find the value of x.

Explanation:

Step1: Apply mid - segment formula

For a trapezoid with bases \(b_1\), \(b_2\) and mid - segment \(m\), the formula is \(m=\frac{b_1 + b_2}{2}\). Here, \(b_1 = 23\), \(b_2=11x + 2\) and \(m = 29\). So, \(29=\frac{23+(11x + 2)}{2}\).

Step2: Cross - multiply

Multiply both sides of the equation by 2: \(29\times2=23 + 11x+2\). Which simplifies to \(58=25 + 11x\).

Step3: Isolate the variable term

Subtract 25 from both sides: \(58 - 25=11x\), so \(33 = 11x\).

Step4: Solve for x

Divide both sides by 11: \(x=\frac{33}{11}=3\).

Answer:

3