Question

points a, b, c, d are collinear and ac = 16 units. what is x? what is ab? what is bd? what is ce?

Explanation:

Step1: Set up equation for AC

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

Step2: Solve for x

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

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

Step5: Find CE

Since $CE=CD + DE$, $CD = 3x - 1$, $DE=2x + 3$, substitute $x = 3$.
$CD=3\times3 - 1=8$, $DE=2\times3+3=6 + 3=9$.
So $CE=8 + 9=17$.

Answer:

$x = 3$
$AB = 10$
$BD = 14$
$CE = 17$