We are asked to determine expressions that are equivalent to the following expression.
-1/2(4-2+8x)
Let's first simplify the given expression. To do it, we will use the Distributive Property. We will distribute - 12 to the terms inside the parentheses.
The given expression is equivalent to -4x-1 and we cannot simplify it any further. Now let's take a look at the possible options and check which of the expressions can also be simplified to -4x-1.
Expression
Is It Equivalent to 4x-1?
-4x-1
Yesâś“
4x-1
No *
3x
No *
-2+1-4x
?
2+1-4x
?
4x+1
No *
Some of the expressions are in simplest forms, so we can already determine if they are equivalent to - 4x-1. Let's simplify the expressions that are not in simplest forms.
Expression
Commutative Property of Addition
Add or Subtract
Is It Equivalent to 4x-1?
-2+1-4x
- 4x-2+1
- 4x-1
Yesâś“
-4x+2+1
- 4x+2+1
- 4x+3
No *
We found that only two expressions are equivalent to the given expression.
rcl
âś“ & - 4x-1 [1 em]
* & 4x-1 [1 em]
* & 3x [1 em]
âś“ & -2+1-4x [1 em]
* & 2+1-4x [1 em]
* & 4x+1 [1 em]
