If DE = 4x + 10, EF = 2x - 1, and DF = 9x - 15, find DF.

DF = 57

Explanation:

DE + EF = DF

DE = 4x + 10

EF = 2x - 1

DF = 9x - 15

First, solve for the given equation. Plug in the corresponding terms to the corresponding variables:

DE + EF = DF

(4x + 10) + (2x - 1) = (9x - 15)

Combine like terms:

(4x + 2x) + (10 - 1) = 9x - 15

6x + 9 = 9x - 15

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 9 & 9x from both sides:

6x (-9x) + 9 (-9) = 9x (-9x) - 15 (-9)

6x - 9x = -15 - 9

-3x = -24

Divide -3 from both sides:

(-3x)/-3 = (-24)/-3

x = -24/-3

x = 8

Plug in 8 for x in the equation given for DF:

DF = 9x - 15

DF = 9(8) - 15

Remember to follow PEMDAS. First multiply, then subtract.

DF = 9(8) - 15

DF = 72 - 15

DF = 57

DF = 57

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