Question

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

Answer 1

DE and EF are segments of the line DF, so they will add up to DF. This can be represented with this equation:

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

Combine like terms:

`4x + 2x = 6x`

`10 + (-1) = 9`

`6x + 9 = 9x - 15`

Add 15 to both sides:

`6x + 24 = 9x`

Subtract 6x from both sides:

`24 = 3x`

Divide both sides by 3 to get x by itself:

`\boxed{x = 8}`

The value of x will be 8.

Plug this value of x into the expression for DF:

`9(8) - 15 = 72 - 15 = \boxed{57}`

DF will equal 57.