if EF=2x-10 FG=3x-9, and EG=21 find the value of x, EF, and FG
To find the value of x, EF, and FG, we can use the given information about the lengths of EF, FG, and EG.
Given:
EF = 2x - 10
FG = 3x - 9
EG = 21
We know that EG is the sum of EF and FG, so we can write the equation: EG = EF + FG
Substituting the given values, we get: 21 = (2x - 10) + (3x - 9)
Now, let's solve the equation for x.
Combine like terms: 21 = 2x - 10 + 3x - 9
Combine constants: 21 = 5x - 19
Isolate the variable term: 21 + 19 = 5x
Combine constants: 40 = 5x
Divide both sides by 5 to solve for x: 40/5 = x
x = 8
Now that we know the value of x, we can substitute it back into the given equations to find the values of EF and FG:
EF = 2x - 10 = 2(8) - 10 = 16 - 10 = 6
FG = 3x - 9 = 3(8) - 9 = 24 - 9 = 15
Therefore, the value of x is 8, EF is 6, and FG is 15.