Question

If EF=2x-14, FG=3x-13, and EG=28. Find the values of x, EF, and FG.

A) I can find the values.
B) I need more information to find the values.
C) I'm not sure how to find the values.
D) The drawing is not to scale, making it difficult to find the values.

Answer 1

To find the values of x, EF, and FG, set up and solve a system of equations using the given information. The values of x, EF, and FG are 11, 8, and 20, respectively.

Step-by-step explanation:

To find the values of x, EF, and FG, we need to set up and solve a system of equations using the given information.

1. Start by setting up the equation for EG: EG = EF + FG. Substitute the given expressions for EF and FG into this equation: 28 = (2x-14) + (3x-13).
2. Combine like terms on the right side: 28 = 2x + 3x - 14 - 13.
3. Combine like terms again: 28 = 5x - 27.
4. Now, isolate the variable x by adding 27 to both sides: 55 = 5x.
5. Divide both sides by 5 to solve for x: 11 = x.
6. Finally, substitute x = 11 back into the expressions for EF and FG to find their values: EF = 2(11) - 14 = 22 - 14 = 8 and FG = 3(11) - 13 = 33 - 13 = 20.