Question

1. the length of $overline{ac}$ is equal to $x + 10$. given the diagram below, determine its actual length.

a 3x - 20 b 3x - 5 c

Explanation:

Step1: Set up equation

Since $AC = AB + BC$ and $AC=x + 10$, $AB = 3x-20$, $BC=3x - 5$, we have the equation $x + 10=(3x-20)+(3x - 5)$.

Step2: Simplify right - hand side

Combine like terms on the right - hand side: $(3x-20)+(3x - 5)=3x+3x-20 - 5=6x-25$. So the equation becomes $x + 10=6x-25$.

Step3: Solve for x

Subtract x from both sides: $10=6x-x-25$, which simplifies to $10 = 5x-25$. Then add 25 to both sides: $10 + 25=5x$, so $35 = 5x$. Divide both sides by 5: $x=\frac{35}{5}=7$.

Step4: Find length of AC

Substitute $x = 7$ into the expression for $AC$: $AC=x + 10=7+10=17$.

Answer:

17