Question

use the figure to solve for x. find ab and bc. a 2x - 2 b x + 5 c 36

Explanation:

Step1: Set up the equation

From the figure, we know that \( AB + BC = AC \). Given \( AB = 2x - 2 \), \( BC = x + 5 \), and \( AC = 36 \), so we can write the equation: \( (2x - 2)+(x + 5)=36 \).

Step2: Simplify the left - hand side

Combine like terms: \( 2x - 2+x + 5=3x + 3 \). So the equation becomes \( 3x+3 = 36 \).

Step3: Solve for x

Subtract 3 from both sides: \( 3x=36 - 3=33 \). Then divide both sides by 3: \( x=\frac{33}{3}=11 \).

Step4: Find AB

Substitute \( x = 11 \) into the expression for \( AB \): \( AB=2x - 2=2\times11-2=22 - 2 = 20 \).

Step5: Find BC

Substitute \( x = 11 \) into the expression for \( BC \): \( BC=x + 5=11 + 5=16 \).

Answer:

\( x = 11 \), \( AB = 20 \), \( BC = 16 \)