If EF = 2x – 12, FG = 3x – 15, and EG = 23, find the values of x, EF, and FG. The drawing is not to scale.

X= 10

EF=8
FG= 15

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To find the values of x, EF, and FG, we need to use the given information and solve the equation(s). Let's start by setting up the equation(s) based on the given information:

Given:
EF = 2x - 12
FG = 3x - 15
EG = 23

Now, we can find the value of x by comparing FG and EG:

FG = EG - EF

Substituting the given values:
3x - 15 = 23 - (2x - 12)

Now, let's solve for x:

3x - 15 = 23 - 2x + 12
3x + 2x = 23 + 12 + 15
5x = 50
x = 50/5
x = 10

Now that we have found the value of x, we can substitute it back into the equations to find the values of EF and FG:

EF = 2x - 12
EF = 2(10) - 12
EF = 20 - 12
EF = 8

FG = 3x - 15
FG = 3(10) - 15
FG = 30 - 15
FG = 15

Therefore, the value of x is 10, EF is 8, and FG is 15.

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