Question

use the figure below to answer questions #11 - 14.
#11: x = ____ *
7
#12: ab = ____ *
39
#13: bc = ____ *
13
#14: ac = ____ *
your answer

Explanation:

Step1: Set up equation based on segment - addition postulate

Since \(AC = AB + BC\), we have \(10x-18=(6x - 3)+(2x - 1)\).

Step2: Simplify the right - hand side of the equation

\((6x - 3)+(2x - 1)=6x+2x-3 - 1=8x-4\). So the equation becomes \(10x-18 = 8x-4\).

Step3: Solve for \(x\)

Subtract \(8x\) from both sides: \(10x-8x-18=8x-8x - 4\), which simplifies to \(2x-18=-4\). Then add 18 to both sides: \(2x-18 + 18=-4 + 18\), so \(2x=14\). Divide both sides by 2: \(x = 7\).

Step4: Find \(AB\)

Substitute \(x = 7\) into the expression for \(AB\): \(AB=6x-3=6\times7-3=42 - 3=39\).

Step5: Find \(BC\)

Substitute \(x = 7\) into the expression for \(BC\): \(BC=2x-1=2\times7-1=14 - 1=13\).

Step6: Find \(AC\)

Substitute \(x = 7\) into the expression for \(AC\): \(AC=10x-18=10\times7-18=70 - 18=52\).

Answer:

#11: \(x = 7\)
#12: \(AB = 39\)
#13: \(BC = 13\)
#14: \(AC = 52\)