Question

4. If DF = 9x - 39, find EF.

Help I’m so confused!!!!

Answer 1

EF =58

Explanation:

from the illustration,

EF =DF - DE

given that DF =9x-39 , DE =47 EF=3x +10

substitute them into the formula,

3x +10=9x-39 - 47

solving for x

3x +10 =9x -86

grouping like terms

3x - 9x =-86 -10

-6x=-96

dividing through by -6

`( - 6x)/( - 6) = ( - 96)/( - 6)`

`x = (96)/(6)`

`x = 16`

but EF=3x+10

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

Answer 2

`\huge\boxed{58}`

First of all, we know that
`DE+EF=DF`, because these are two segments that make up one larger segment.

Write this as an equation.

`DE+EF=DF`

`47+(3x+10)=9x-39`

Remove the parentheses.
`47+3x+10=9x-39`

Combine the like terms.
`3x+57=9x-39`

Subtract
`9x` from both sides.
`-6x+57=-39`

Subtract
`57` from both sides.
`-6x=-96`

Divide both sides by
`-6`.
`x=16`

Now, find
`EF`.

`3x+10`

`3(16)+10`

Multiply.
`48+10`

Add.
`\boxed{58}`