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QuestionFind the length of segment CD‾\overline{C D} if CD=xC D=x, BC=5x−5B C=5x-5, and BD=2x+7B D=2x+7.

Studdy Solution

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 equationBD=BC+CDBD = BC + CD

STEP 3

Now, we can substitute the given expressions for BD, BC, and CD into the equation.
2x+7=(5x−5)+x2x +7 = (5x -5) + x

STEP 4

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

STEP 5

To solve for x, we can first subtract2x from both sides of the equation.
7=4x−57 =4x -5

STEP 6

Next, add5 to both sides of the equation to isolate the term with x.
12=4x12 =4x

STEP 7

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

STEP 8

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

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