Question

points a, b, c, d, and e are collinear. a b c d e 22. if ac = 16, what is x? 23. what is ab? 24. what is bd? 25. what is ce?

Explanation:

Step1: Set up equation for AC

Since $AC = AB + BC$ and $AB=x + 7$, $BC = 2x$, and $AC = 16$, we have the equation $(x + 7)+2x=16$.
Combining like - terms gives $3x+7 = 16$.

Step2: Solve for x

Subtract 7 from both sides of the equation $3x+7 = 16$:
$3x+7-7=16 - 7$, so $3x=9$.
Divide both sides by 3: $\frac{3x}{3}=\frac{9}{3}$, then $x = 3$.

Step3: Find AB

Substitute $x = 3$ into the expression for $AB$. Since $AB=x + 7$, then $AB=3 + 7=10$.

Step4: Find BD

Since $BD=BC + CD$, $BC = 2x$ and $CD=3x - 1$, substitute $x = 3$.
$BC=2\times3 = 6$ and $CD=3\times3-1=9 - 1 = 8$.
So $BD=6 + 8=14$.

Step5: Find CE

Since $CE=CD + DE$, $CD=3x - 1$ and $DE=2x+1$, substitute $x = 3$.
$CD=3\times3-1=8$ and $DE=2\times3 + 1=6 + 1=7$.
So $CE=8 + 7=15$.

Answer:

1. $x = 3$
2. $AB = 10$
3. $BD = 14$
4. $CE = 15$