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.