If EF=3x-5, FG=4x-6, and EG=17, find the values of x, EF and FG. PLEASE HELP!!!!!

To find the values of x, EF, and FG, we can use the given information and write equations based on the lengths of the line segments.

1. Start by considering the entire line segment EG, which can be split into two smaller segments: EF and FG.

2. Since EG = EF + FG, we can substitute the given lengths into this equation:
17 = EF + FG

3. We also have the information that EF = 3x - 5 and FG = 4x - 6. Substitute these expressions into the previous equation:
17 = (3x - 5) + (4x - 6)

4. Now, simplify the equation by combining like terms:
17 = 3x + 4x - 5 - 6
17 = 7x - 11

5. To isolate the variable x, add 11 to both sides of the equation:
17 + 11 = 7x
28 = 7x

6. Divide both sides of the equation by 7 to solve for x:
x = 28 / 7
x = 4

Now that we have found the value of x, we can substitute it back into the expressions for EF and FG to find their values.

7. EF = 3x - 5 = 3(4) - 5 = 12 - 5 = 7
8. FG = 4x - 6 = 4(4) - 6 = 16 - 6 = 10

Therefore, the value of x is 4, EF is 7, and FG is 10.