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QuestionFind BCBC given AB=9AB=9, AC=5x−1AC=5x-1, and BC=2x+2BC=2x+2.

Studdy Solution

STEP 1

Assumptions1. The length of line segment AB is9 units. . The length of line segment AC is represented by the expression5x -1.
3. The length of line segment BC is represented by the expressionx +.
4. The line segments AB, AC, and BC form a straight line (since they are part of the same line).

STEP 2

Since AB, AC, and BC form a straight line, the sum of the lengths of AB and BC should be equal to the length of AC. We can write this as an equationAB+BC=ACAB + BC = AC

STEP 3

Now, plug in the given values and expressions for AB, BC, and AC to form the equation.
9+(2x+2)=5x−19 + (2x +2) =5x -1

STEP 4

implify the left side of the equation by combining like terms.
11+2x=x−111 +2x =x -1

STEP 5

Rearrange the equation to isolate the variable x on one side. Subtract2x from both sides.
11=3x−111 =3x -1

STEP 6

Next, add1 to both sides of the equation to isolate3x on one side.
12=3x12 =3x

STEP 7

Finally, divide both sides of the equation by3 to solve for x.
x=12/3x =12 /3

STEP 8

Calculate the value of x.
x=12/3=4x =12 /3 =4

STEP 9

Now that we have the value of x, we can substitute it into the expression for BC to find the length of BC.
BC=2x+2BC =2x +2

STEP 10

Substitute the value of x into the expression for BC.
BC=2(4)+2BC =2(4) +2

STEP 11

Calculate the length of BC.
BC=(4)+=10BC =(4) + =10The length of BC is10 units.

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