Math Snap

STEP 1

Assumptions1. Line $y$ bisects $AC$, which means $AB = BC$.
. The length of $AB$ is given by $4-5x$.
3. The length of $BC$ is given by $x+25$.

STEP 2

Since $AB = BC$, we can set the expressions for $AB$ and $BC$ equal to each other and solve for $x$.
$$4-5x =2x+25$$

STEP 3

To isolate $x$, we can start by adding $5x$ to both sides of the equation to get rid of the negative $5x$ on the left side.
$$=7x +25$$

STEP 4

Next, subtract $25$ from both sides to isolate $7x$ on one side of the equation.
$$-21 =7x$$

STEP 5

Finally, divide both sides by $7$ to solve for $x$.
$$x = -3$$

STEP 6

Now that we have the value of $x$, we can substitute it into the expressions for $AB$ and $BC$ to find the lengths of these segments.
For $AB$, we have$$AB =4 -5(-3)$$

STEP 7

Calculate the length of $AB$.
$$AB =4 +15 =19$$

STEP 8

For $BC$, we have$$BC =2(-3) +25$$

STEP 9

Calculate the length of $BC$.
$$BC = -6 +25 =19$$

STEP 10

Since $AB = BC$, and line $y$ bisects $AC$, the length of $AC$ is simply $2 \times AB$ or $2 \times BC$.
$$AC =2 \times AB$$

STEP 11

Substitute the value of $AB$ into the equation to find $AC$.
$$AC = \times19$$

Calculate the length of $AC$.
$$AC =2 \times19 =38$$So, the length of $AC$ is $38$.