Question

1. segment ac has a point b between points a and c. ab = 4x + 2, bc = 3x - 1, and ac = 9x - 11. draw and label your figure, then solve for x find the measure of each segment: ab = □ bc = □ ac = □

Explanation:

Step1: Use segment addition postulate

Since \(AC = AB + BC\), substitute the given expressions: \(9x - 11=(4x + 2)+(3x - 1)\).

Step2: Simplify the right - hand side

Simplify \((4x + 2)+(3x - 1)\) to \(4x+2 + 3x-1=7x + 1\). So the equation becomes \(9x-11 = 7x+1\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(9x-7x-11=7x - 7x+1\), which gives \(2x-11 = 1\). Then add \(11\) to both sides: \(2x-11 + 11=1 + 11\), so \(2x=12\). Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Step4: Find \(AB\)

Substitute \(x = 6\) into \(AB = 4x+2\). Then \(AB=4\times6+2=24 + 2=26\).

Step5: Find \(BC\)

Substitute \(x = 6\) into \(BC = 3x-1\). Then \(BC=3\times6-1=18 - 1=17\).

Step6: Find \(AC\)

Substitute \(x = 6\) into \(AC = 9x-11\). Then \(AC=9\times6-11=54 - 11=43\).

Answer:

\(x = 6\), \(AB = 26\), \(BC = 17\), \(AC = 43\)