Answer:
A, B, and E
Step-by-step explanation:
Let's look through each of the answer choices.
A) 2(x + 2) + 2 = 2(x + 3) + 1
Simplify this by expanding out the parentheses:
2x + 2 * 2 + 2 = 2x + 2 * 3 + 1
2x + 4 + 2 = 2x + 6 + 1
2x + 6 = 2x + 7
6 = 7
Well, we know that 6 is NOT equal to 7, so this has no solutions.
B) 2x + 3(x + 5) = 5(x – 3)
Simplify this by expanding out the parentheses:
2x + 3x + 3 * 5 = 5x - 5 * 3
5x + 15 = 5x - 15
15 = -15
Again, we know that 15 is NOT equal to -15, so this also has no solutions.
C) 4(x + 3) = x + 12
Simplify this by expanding out the parentheses:
4x + 4 * 3 = x + 12
4x + 12 = x + 12
3x = 0
x = 0
This actually does have a solution when x = 0, so eliminate this.
D) 4 – (2x + 5) = (–4x – 2)
Simplify this by expanding out the parentheses:
4 - 2x - 5 = -4 - 2
-2x - 1 = -6
-2x = -5
x = 2.5
This also has a solution when x = 2.5, so eliminate this.
E) 5(x + 4) – x = 4(x + 5) – 1
Simplify this by expanding out the parentheses:
5x + 5 * 4 - x = 4x + 4 * 5 - 1
4x + 20 = 4x + 19
20 = 19
Here, we know that 20 is NOT equal to 19, so this has no solution.
Hope this helps!
