Math Snap

STEP 1

Assumptions1. Point C is on line segment BD.
. The length of CD is represented by x.
3. The length of BC is represented by5x -5.
4. The length of BD is represented byx +7.

STEP 2

We know that the length of line segment BD is equal to the sum of the lengths of line segments BC and CD. We can write this as an equation$$BD = BC + CD$$

STEP 3

Now, we can substitute the given expressions for BD, BC, and CD into the equation.
$$2x +7 = (5x -5) + x$$

STEP 4

implify the right side of the equation.
$$2x +7 =6x -$$

STEP 5

To solve for x, we can first subtract2x from both sides of the equation.
$$7 =4x -5$$

STEP 6

Next, add5 to both sides of the equation to isolate the term with x.
$$12 =4x$$

STEP 7

Finally, divide both sides of the equation by4 to solve for x.
$$x =12 /4$$

Calculate the value of x.
$$x =12 /4 =3$$So, the numerical length of line segment CD is3 units.