Which of the following expressions are not equivalent to the expression 2x + 2 - 5x + 7 - 3? Select all that apply.
(1 point)
2x + 11 - 5x
-3x + 6
-
3x - 6
2(x + 1)- 5x + 4
2(x + 1)- 5 over 2x + 2
Please explain
To determine which expressions are not equivalent to 2x + 2 - 5x + 7 - 3, we can simplify each expression and compare the results.
Starting with 2x + 2 - 5x + 7 - 3:
Combine like terms: (2x - 5x) + (2 + 7 - 3) = -3x + 6
Now let's simplify each given expression and compare:
1) 2x + 11 - 5x:
Combine like terms: (2x - 5x) + 11 = -3x + 11
This expression is not equivalent to -3x + 6.
2) -3x + 6:
This is already simplified and equivalent to the original expression.
This expression is equivalent to -3x + 6.
3) 3x - 6:
This expression is not equivalent to -3x + 6.
4) 2(x + 1) - 5x + 4:
Apply the distributive property: 2x + 2 - 5x + 4 - 5x + 4
Combine like terms: (2x - 5x - 5x) + (2 + 4 + 4) = -8x + 10
This expression is not equivalent to -3x + 6.
5) 2(x + 1) - 5 over 2x + 2:
This expression is not equivalent to -3x + 6.
Therefore, the expressions that are not equivalent to 2x + 2 - 5x + 7 - 3 are:
1) 2x + 11 - 5x
3) 3x - 6
4) 2(x + 1) - 5x + 4
5) 2(x + 1) - 5 over 2x + 2
How is 5) 2(x + 1) - 5 over 2 (5/2) x+ 2 not equivalent?
Apologies for the mistake in the explanation. Let's simplify expression 5) correctly and compare it to the original expression.
5) 2(x + 1) - 5 over 2 (5/2) x+ 2:
First, simplify the expression within the parentheses by applying the distributive property: 2x + 2.
Next, simplify the expression -5 over 2 (5/2) x+ 2:
To simplify this expression, we need to first simplify the term -5 over 2 (5/2) x. Multiplying the fractions:
-5/2 * 5/2 = -25/4. Therefore, the term simplifies to -25/4x.
Now, our expression becomes: 2x + 2 - 25/4x + 2.
To combine like terms, we add the coefficients of x:
2x - 25/4x = (8x/4) - (25/4)x = (8x - 25x)/4 = -17x/4
The expression is simplified to: -17x/4 + 2 + 2 = -17x/4 + 4
Comparing this simplified expression to the original:
-17x/4 + 4 is not equivalent to -3x + 6.
Therefore, the correct answer is:
5) 2(x + 1) - 5 over 2 (5/2) x+ 2 is not equivalent to 2x + 2 - 5x + 7 - 3.
2(x + 1)-3 x + 2
To simplify the expression 2(x + 1) - 3x + 2, let's apply the distributive property:
2(x + 1) - 3x + 2
= 2 * x + 2 * 1 - 3x + 2
= 2x + 2 - 3x + 2
Next, let's combine like terms by adding or subtracting coefficients of the same variable:
2x + 2 - 3x + 2
= (2x - 3x) + (2 + 2)
= -x + 4
The simplified expression is -x + 4.
Therefore, the expression 2(x + 1) - 3x + 2 is not equivalent to the original expression 2x + 2 - 5x + 7 - 3.
To determine which of the given expressions are not equivalent to the expression 2x + 2 - 5x + 7 - 3, we need to simplify each expression and compare them.
Let's simplify each expression step-by-step:
1. Simplify 2x + 11 - 5x:
2x + 11 - 5x = -3x + 11 ⟶ Expression 1
2. Simplify -3x + 6:
-3x + 6 = -3x + 6 ⟶ Expression 2
3. Simplify 3x - 6:
3x - 6 = 3x - 6 ⟶ Expression 3
4. Simplify 2(x + 1) - 5x + 4:
2(x + 1) - 5x + 4 = 2x + 2 - 5x + 4 ⟶ Expression 4
5. Simplify 2(x + 1) - 5 / 2x + 2:
This expression is a bit unclear. It could be interpreted in two ways:
a. 2(x + 1) - (5 / 2x) + 2 ⟶ Expression 5a
b. (2(x + 1) - 5) / (2x + 2) ⟶ Expression 5b
Now let's compare each expression to the original expression:
Expression 1: -3x + 11 ⟶ Not equivalent to the original expression.
Expression 2: -3x + 6 ⟶ Not equivalent to the original expression.
Expression 3: 3x - 6 ⟶ Not equivalent to the original expression.
Expression 4: 2x + 2 - 5x + 4 ⟶ Equivalent to the original expression.
Expression 5a: 2(x + 1) - (5 / 2x) + 2 ⟶ Not equivalent to the original expression.
Expression 5b: (2(x + 1) - 5) / (2x + 2) ⟶ Equivalent to the original expression.
Therefore, the expressions that are not equivalent to the original expression are:
- Expression 1: -3x + 11
- Expression 2: -3x + 6
- Expression 3: 3x - 6
- Expression 5a: 2(x + 1) - (5 / 2x) + 2
To determine which expressions are not equivalent to the given expression 2x + 2 - 5x + 7 - 3, we need to simplify each expression and compare the results.
Let's simplify each expression step by step:
Expression 1: 2x + 11 - 5x
Combine like terms:
2x - 5x = -3x
The simplified expression is -3x + 11.
Expression 2: -3x + 6
This expression is already simplified, so no further steps are necessary.
Expression 3: 3x - 6
This expression is different from the original expression. We can simplify it further:
-6 + 3x is equivalent to 3x - 6.
Expression 4: 2(x + 1) - 5x + 4
Distribute 2 to (x + 1):
2x + 2 - 5x + 4
Combine like terms:
2x - 5x = -3x
2 + 4 = 6
The simplified expression is -3x + 6.
Expression 5: 2(x + 1) - 5 over 2x + 2
This expression is not properly written. It seems to be a fraction where part of it is in the numerator and part of it is in the denominator. We can't directly compare it to the original expression. It needs to be properly simplified or reformulated.
Based on the simplifications, the expressions that are not equivalent to 2x + 2 - 5x + 7 - 3 are:
Expression 3: 3x - 6
Expression 5: 2(x + 1) - 5 / 2x + 2 (reformulate or simplify it before comparing)
So, Expression 3 and Expression 5 are not equivalent to the original expression.