Answer:
X =8
Step-by-step explanation:
DF = DE + EF
15 = X+1 + X-2
16 = 2X
X = 8
The number is x
it is negative
the square is 28 more than 3 times itself
x²=28+3x
minus (28+3x)
x²-3x-28=0
factor
(x-7)(x+4)=0
set to zero
x-7=0
x=7
this is not the answer because we were told the number was negative
x+4=0
x=-4
correct
the number is -4
test
(-4)²=28+3(-4)
16=28-12
16=16
check
the number is -4
Simplify both sides if needed. The left-hand side needs simplification.
4(x - 6)

-2x + 6
4x - 24

-2x + 6
All is left to do is add and subtract to get the x variable all alone.
4x - 24

-2x + 6
6x - 24

6 <-- Add 2x to both sides
6x

30 <-- Add 24 to both sides
x

5 <-- Divide both sides by 6
In order to be in the solution set, x has to be less than or equal to 5.
In interval notation: [5, -∞)