Which of the following expressions are equivalent to the expression 3x + 4 - 5x + 6 - 2? Select all that apply.
-2x + 8
4 - 2x + 4
8x +8
-2x + 10 - 2
-2x + 12
-2x + 8
4 - 2x + 4
-2x + 12
To determine which of the given expressions are equivalent to 3x + 4 - 5x + 6 - 2, we need to simplify the expression using the rules of combining like terms and order of operations.
First, let's regroup the terms with the same variable:
3x - 5x + 4 + 6 - 2
Next, combine like terms:
(-2x) + 10
Now, we can compare this simplified expression with the given options to determine which are equivalent.
Let's go through each option:
Option 1: -2x + 8
This option is equivalent because -2x + 10 simplifies to -2x + 8.
Option 2: 4 - 2x + 4
This option is not equivalent because there is an additional 4 term that was not present in the original expression.
Option 3: 8x + 8
This option is not equivalent because there is no x term in the original expression.
Option 4: -2x + 10 - 2
This option is equivalent because it matches the simplified expression we obtained.
Option 5: -2x + 12
This option is not equivalent because there is no constant term of 12 in the original expression.
Therefore, the equivalent expressions are:
-2x + 8
-2x + 10 - 2
So, the correct options are:
-2x + 8
-2x + 10 - 2
To find equivalent expressions, we can simplify the given expression step-by-step:
Given expression: 3x + 4 - 5x + 6 - 2
Step 1: Combine like terms: (-5x + 3x) + (4 + 6 - 2) = -2x + 8
Step 2: Simplify further: -2x + 8
From the given options:
-2x + 8 is equivalent to the expression 3x + 4 - 5x + 6 - 2.
Therefore, the equivalent expression is -2x + 8.
The expressions -2x + 8x + 8 and -2x + 10 - 2 are not equivalent to the given expression.
Therefore, the correct answer is:
-2x + 8