Question

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

Answer 1

DF = 57

Explanation:

From the given information on the line segments we can write the equation

DF = DE + EF ( substituting the values into the equation )

9x - 15 = 4x + 10 + 2x - 1

9x - 15 = 6x + 9 ( subtract 6x from both sides )

3x - 15 = 9 ( add 15 to both sides )

3x = 24 ( divide both sides by 3 )

x = 8

DF = 9x - 15 = (9 × 8) - 15 = 72 - 15 = 57

Answer 2

DF= 57

Explanation:

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

DF= DE + EF

Now we plug in the expression given for DE, EF and DF in the equation

`DF= DE + EF`

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

Now we solve the equation for x

Combine like terms ,

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

`9x-15=6x+9`

Subtract 6x from both sides

`3x-15=9`

Add 15 from both sides

`3x=24`

Divide both sides by 3

So x= 8

Now we plug in x for 8 in DF

`DF= 9x-15`

`DF= 9(8)-15=57`