Question

Points E, F, and G are collinear. Point F lies between E and G. If Latex: EF:=4x-15,:FG:=5x+7:and:EG:=46,:E F = 4 x − 15 , F G = 5 x + 7 a n d E G = 46 ,find the value of Latex: EF.E F . LaTeX: EF=:E F = _________

Answer 1

To find the value of EF, use the equation EF + FG = EG and solve for x. Then substitute the value of x back into the equation to find EF. EF = 9.

Step-by-step explanation:

Given that points E, F, and G are collinear and F lies between E and G, we can write the equation EF + FG = EG.

Substituting the given values: 4x - 15 + 5x + 7 = 46.

Combining like terms and solving for x: 9x - 8 = 46.

Adding 8 to both sides: 9x = 54.

Dividing both sides by 9: x = 6.

Now we can find the value of EF by substituting x back into the equation: EF = 4(6) - 15

= 24 - 15

= 9.