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
The equivalent expressions are:
-2x + 8
4 - 2x + 4
-2x + 12
To find which expressions are equivalent to 3x + 4 - 5x + 6 - 2, you need to simplify the given expression by combining like terms.
Step 1: Group all the terms with x together. In this case, we have 3x and -5x.
3x - 5x = -2x
Step 2: Combine all the constant terms (with no x). In this case, we have 4, 6, and -2.
4 + 6 - 2 = 8
Now, the simplified expression is -2x + 8.
Let's check each answer option:
-2x + 8: This is the answer we got after simplifying the expression, so it is equivalent.
4 - 2x + 4: Rearranging the terms, we get 4 + 4 - 2x = 8 - 2x.
This expression is NOT equivalent to the original expression because it has a constant term of 8, whereas the original expression had a constant term of 8 (which we simplified to).
8x + 8: This expression has a different variable term (8x instead of -2x), so it is NOT equivalent.
-2x + 10 - 2: Rearranging the terms, we get -2x - 2 + 10 = 8 - 2x.
This expression is NOT equivalent to the original expression because it has a constant term of 8, whereas the original expression had a constant term of 8 (which we simplified to).
-2x + 12: This expression has a different constant term (12 instead of 8), so it is NOT equivalent.
Therefore, the expressions that are equivalent to 3x + 4 - 5x + 6 - 2 are -2x + 8.
To find which expressions are equivalent to the given expression 3x + 4 - 5x + 6 - 2, we can simplify it step-by-step.
Step 1: Combine like terms with the same variable x:
3x - 5x = -2x
Step 2: Combine the constants:
4 + 6 - 2 = 8
Therefore, the simplified expression is -2x + 8.
Now let's check the options:
-2x + 8: This is the simplified expression we obtained, so it is equivalent to the given expression.
4 - 2x + 4: Rearranging the terms, we get 4 + 4 - 2x = 8 - 2x. This is not equivalent to the given expression because we obtained -2x + 8 instead.
8x + 8: There is no term with x in the given expression, so this is not equivalent.
-2x + 10 - 2: Rearranging the terms, we get 10 - 2 - 2x = 8 - 2x. This is not equivalent to the given expression because we obtained -2x + 8 instead.
-2x + 12: This is not equivalent to the given expression because we obtained -2x + 8 instead.
Therefore, the expressions -2x + 8 is the only one equivalent to the given expression.