Question

$\overline{ab}$ is congruent to $\overline{cd}$. solve for x.

a
3(2x - 11)
f
23
b
c
32
d
o a. x = 3.3
o c. x = 28
o d. x = 7
o b. x = 9

Explanation:

Step1: Use the congruent segments property

Since \(\overline{AB}\cong\overline{CD}\), then \(AB = CD\).
From the figure, \(AB=3(2x - 11)+23\) and \(CD = 32\). So, \(3(2x - 11)+23=32\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(3\times(2x)-3\times11 + 23=32\), which simplifies to \(6x-33 + 23=32\).

Step3: Combine like terms

Combine the constant terms: \(6x-(33 - 23)=32\), so \(6x-10 = 32\).

Step4: Isolate the term with \(x\)

Add \(10\) to both sides of the equation: \(6x-10 + 10=32+10\), which gives \(6x=42\).

Step5: Solve for \(x\)

Divide both sides by \(6\): \(x=\frac{42}{6}\).

Answer:

\(x = 7\), so the answer is D.