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If EF = 3x − 17, FG = 4x − 16,and EG = 23, find the values of x, EF, and FG.

(The drawing is not to scale.)

If EF 3x 17 FG 4x 16and EG 23 find the values of x EF and FG The drawing is not to scale class=

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Answer:

Option C is correct.

The value of x = 8 , EF = 7 and FG = 16

Step-by-step explanation:

Given : [tex]EF = 3x-17[/tex] , [tex]FG = 4x-16[/tex] and [tex]EG = 23[/tex]

From the given figure.

EG = EF + EG

Substitute the given values we have;

[tex]23 = 3x-17+4x-16[/tex]

Combine like terms;

[tex]23 = 7x-33[/tex]

Add 33 both sides we get;

[tex]56= 7x[/tex]

Divide both sides by 7 we get;

8 = x

or

x = 8

EF = 3x -17 = 3(8) -17 = 24 -17 = 7

FG = 4x-16 = 4(8) -16 = 32-16 = 16

therefore, the value of x = 8 , EF = 7 and FG = 16

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