Studdy AI Logo
Math

QuestionFind xx if points A, B, C are collinear with BC=x+1BC=x+1, AB=2x+2AB=2x+2, and AC=12AC=12.

Studdy Solution

STEP 1

Assumptions1. Points A, B and C are collinear. . Point B is between A and C.
3. The length of segment BC is given by the equation BC=x+1BC = x +1.
4. The length of segment AB is given by the equation AB=x+AB =x +.
5. The length of segment AC is given as12 units.

STEP 2

Since points A, B and C are collinear and B is between A and C, we can say that the length of segment AC is equal to the sum of the lengths of segments AB and BC.
AC=AB+BCAC = AB + BC

STEP 3

Now, we can substitute the given equations for AB, BC, and AC into the equation from2.
12=(2x+2)+(x+1)12 = (2x +2) + (x +1)

STEP 4

implify the right side of the equation by combining like terms.
12=3x+312 =3x +3

STEP 5

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting3 from both sides of the equation.
12−3=3x12 -3 =3x

STEP 6

implify the left side of the equation.
9=3x9 =3x

STEP 7

Finally, divide both sides of the equation by3 to solve for x.
x=9/3x =9 /3

STEP 8

Calculate the value of x.
x=3x =3So, the value of x is3.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord