EF = 3x-16, FG = 2x-7, and EG = 17, find the values of x, EF, and FG
assuming F is between E and G,
EF+FG=EG
3x-16 + 2x-7 = 17
5x = 40
x = 8
EF = 8
FG = 9
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To find the values of x, EF, and FG, we will use the given information:
1. We know that EF = 3x - 16.
2. Similarly, FG = 2x - 7.
3. Also, EG = 17.
To solve for x, we can set EF equal to FG since they both represent the same line segment:
3x - 16 = 2x - 7.
Now, we will solve this equation step-by-step to find the value of x:
1. Subtract 2x from both sides of the equation to isolate x:
3x - 2x - 16 = 2x - 2x - 7.
Simplifying the equation: x - 16 = -7.
2. Add 16 to both sides of the equation to isolate x:
x - 16 + 16 = -7 + 16.
Simplifying the equation: x = 9.
So, the value of x is 9.
Now, we can substitute the value of x into EF and FG to find their values:
1. For EF: EF = 3(9) - 16 = 27 - 16 = 11.
So, EF = 11.
2. For FG: FG = 2(9) - 7 = 18 - 7 = 11.
So, FG = 11.
Therefore, the values are as follows:
x = 9,
EF = 11,
FG = 11.
To find the values of x, EF, and FG, we need to use the information given about EF, FG, and EG and set up equations that will allow us to solve for x.
Given:
EF = 3x - 16
FG = 2x - 7
EG = 17
We can start by using the fact that EF + FG = EG. Substituting the given values, we get:
(3x - 16) + (2x - 7) = 17
Now, we can solve this equation for x:
Combine the like terms on the left side of the equation:
5x - 23 = 17
Add 23 to both sides of the equation to isolate the variable:
5x = 17 + 23
5x = 40
Next, divide both sides of the equation by 5 to solve for x:
x = 40 / 5
x = 8
Now that we have the value of x, we can substitute it back into the original equations to find EF and FG.
For EF:
EF = 3x - 16
EF = 3(8) - 16
EF = 24 - 16
EF = 8
For FG:
FG = 2x - 7
FG = 2(8) - 7
FG = 16 - 7
FG = 9
Therefore, the values of x, EF, and FG are:
x = 8
EF = 8
FG = 9