A student claims that 8x-2(4+3x) is equivalent to 3x The student's steps are shown below.
Steps provided by the student:
1. Start with 8x-2(4+3x)
2. Use the distributive property to simplify -2(4+3x) to -8-6x
3. Combine like terms to get 8x+(-8-6x)
4. Simplify further by adding the like terms to get 2x-8
5. Simplify completely to get 3x-8
The student's claim is incorrect. The expression 8x-2(4+3x) simplifies to 2x-8, not 3x.
Would 2x -8 be -6 then?
No, 2x - 8 is not equal to -6.
The expression 2x - 8 cannot be simplified further unless more information about the value of 'x' is given. It is a simplified form of the original expression 8x - 2(4 + 3x).
The expression -6 is not obtained anywhere in the given steps or the simplified expression.
To determine if the student's claim is correct, let's follow the steps they provided:
Step 1: Start with the expression 8x-2(4+3x).
Step 2: Distribute the -2 to both terms inside the parentheses.
-2(4) = -8
-2(3x) = -6x
The expression becomes: 8x - 8 - 6x
Step 3: Combine like terms.
In this case, both terms have an 'x' variable, so we can combine them.
8x - 6x = 2x
The expression becomes: 2x - 8
The student's final result is 2x - 8, not 3x. Therefore, their claim that 8x-2(4+3x) is equivalent to 3x is incorrect.
To determine if the student's claim is correct, we can simplify the expression 8x - 2(4 + 3x) and see if it simplifies to 3x. Let's follow the student's steps and determine if they are correct:
Expression: 8x - 2(4 + 3x)
Step 1: Distribute the -2 to the terms inside the parentheses.
This means we multiply -2 by 4 and -2 by 3x.
8x - 2(4) - 2(3x)
Simplifying the multiplication: -2(4) = -8 and -2(3x) = -6x.
8x - 8 - 6x
Step 2: Combine like terms.
We combine the x terms and the constants.
(8x - 6x) - 8
Simplifying the subtraction: 8x - 6x = 2x
2x - 8
Now, we have simplified the expression based on the steps the student provided.
We can see that the final simplified expression is 2x - 8, which is not equivalent to 3x. Therefore, the student's claim is incorrect, and the initial expression 8x - 2(4 + 3x) is not equivalent to 3x.