Question

If Ef=2x-8, FG = 3x - 14, and EG = 28, find the values of x, EF, and FG.

a) x = 12, EF = 16, FG = 22
b) x = 10, EF = 12, FG = 16
c) x = 8, EF = 10, FG = 12
d) x = 14, EF = 18, FG = 24"

Answer 1

By setting up and solving the equation EF + FG = EG, where EF = 2x - 8, FG = 3x - 14, and EG = 28, we find that x equals 10. Subsequently, EF and FG are calculated to be 12 and 16, respectively.

Step-by-step explanation:

To find the values of x, EF, and FG, we can use the given equation EF = 2x - 8 and FG = 3x - 14 along with the information that EG = 28. Since EF + FG = EG, we can set up the equation 2x - 8 + 3x - 14 = 28. Solving for x gives us:

1. Combine like terms: 5x - 22 = 28
2. Add 22 to both sides: 5x = 50
3. Divide by 5: x = 10

Now that we have x, we can find EF and FG by substituting x into their respective equations:

• EF = 2(10) - 8 = 20 - 8 = 12
• FG = 3(10) - 14 = 30 - 14 = 16

So, the correct answer is b) x = 10, EF = 12, FG = 16.