Algebra 1 Unit 2 Test Question 1 - Which of the following expressions are not equivalent to the expression 2x + 2 - 5x + 7 - 3? a) 2x +11 - 5x b) -3x +6 c) 3x - 6 d) 2(x+1) - 5x +4 e) 2 (x + 1) - 5/2x + 2
The expression 2x + 2 - 5x + 7 - 3 can be simplified by combining like terms:
2x - 5x + 2 + 7 - 3 = -3x + 6
Therefore, the original expression is equivalent to the expression in answer choice b) -3x + 6.
The other answer choices are:
a) 2x + 11 - 5x = -3x + 11
c) 3x - 6
d) 2(x + 1) - 5x + 4 = 2x + 2 - 5x + 4 = -3x + 6
e) 2(x + 1) - 5/2x + 2 = 2x + 2 - (5/2)x + 2 = (4/2)x + 4 = 2x + 4
Therefore, the expressions not equivalent to 2x + 2 - 5x + 7 - 3 are:
c) 3x - 6
e) 2(x + 1) - 5/2x + 2
Would the answer also include a) 2x + 11 - 5x?
I apologize for the confusion. Yes, the expression a) 2x + 11 - 5x is also not equivalent to 2x + 2 - 5x + 7 - 3. The correct answer should be:
a) 2x + 11 - 5x = -3x + 11
c) 3x - 6
e) 2(x + 1) - 5/2x + 2
Thank you for catching that mistake.
To solve this question, we need to simplify each expression and then compare it to the original expression, 2x + 2 - 5x + 7 - 3.
Let's simplify each of the given expressions and see if they are equivalent or not:
a) 2x + 11 - 5x
Simplifying this expression, we get: -3x + 11.
b) -3x + 6
This expression is already simplified.
c) 3x - 6
This expression is already simplified.
d) 2(x + 1) - 5x + 4
Expanding this expression, we get: 2x + 2 - 5x + 4
Combining like terms, we get: -3x + 6.
e) 2 (x + 1) - 5/2x + 2
Expanding the expression, we get: 2x + 2 - (5/2)x + 2
Combining like terms, we get: (4 - 5/2)x + 4
Simplifying the expression, we have: (8/2 - 5/2)x + 4
Combining like terms, we get: (3/2)x + 4.
Now, let's compare each simplified expression to the original expression:
-3x + 11.
-3x + 6.
3x - 6.
-3x + 6.
(3/2)x + 4.
Comparing each expression to the original expression, we can see that only the expression (3/2)x + 4 is not equivalent to the original expression 2x + 2 - 5x + 7 - 3.
Therefore, the answer is e) 2 (x + 1) - 5/2x + 2.
To determine which of the given expressions are not equivalent to the expression 2x + 2 - 5x + 7 - 3, we need to simplify each option and compare it to the given expression. Let's go through each option one by one:
a) 2x + 11 - 5x:
To simplify this expression, we can combine like terms. So, 2x - 5x gives us -3x. Therefore, the simplified form of this expression is -3x + 11.
b) -3x + 6:
No further simplification is needed for this expression since there are no like terms to combine.
c) 3x - 6:
Again, no further simplification is needed for this expression.
d) 2(x + 1) - 5x + 4:
To simplify this expression, we can start by distributing the 2 into the parentheses: 2x + 2 - 5x + 4. Next, combining the like terms gives us -3x + 6.
e) 2(x + 1) - (5/2)x + 2:
Let's distribute the 2 into the parentheses: 2x + 2 - (5/2)x + 2. We can combine the like terms -5/2x and 2x to get -1/2x. Therefore, the simplified form of this expression is -1/2x + 4.
Now, let's compare each simplified expression to the original expression 2x + 2 - 5x + 7 - 3:
a) -3x + 11 ≠ 2x + 2 - 5x + 7 - 3 (not equivalent)
b) -3x + 6 = 2x + 2 - 5x + 7 - 3 (equivalent)
c) 3x - 6 ≠ 2x + 2 - 5x + 7 - 3 (not equivalent)
d) -3x + 6 = 2x + 2 - 5x + 7 - 3 (equivalent)
e) -1/2x + 4 ≠ 2x + 2 - 5x + 7 - 3 (not equivalent)
So, the expressions that are not equivalent to the original expression are a) 2x + 11 - 5x and c) 3x - 6.