A student claims that 8x - 2(4+3x) is equivalent to 3x. The student steps are shown below.
Expression: 8x - 2(4+3x)
Step 1: 8x - 8 + 3x
Step 2: 8x + 3x - 8
Step 3:11x - 8
Step 4: 3x
To determine whether the student's claim is correct, let's go through the steps one by one:
Step 1: 8x - 8 + 3x
To distribute the -2, we multiply it by each term inside the bracket:
= 8x - 8 + (3x * -2)
= 8x - 8 - 6x
Step 2: 8x + 3x - 8 - 6x
Combine like terms:
= 8x + 3x - 6x - 8
Note: When combining terms, add or subtract the coefficients of the same variable.
Step 3: 11x - 8
Combine like terms:
= (8x + 3x - 6x) - 8
= 11x - 8
Step 4: 3x
Now, let's compare the original expression to the claimed equivalent expression:
8x - 2(4+3x) vs. 3x
The expressions are not equivalent. The student's claim is incorrect.
To determine if the expression 8x - 2(4+3x) is equivalent to 3x, we need to simplify the expression using the given steps.
Step 1: Applying the distributive property, we multiply -2 to both terms inside the parentheses.
8x - 2(4+3x) = 8x - 8 - 6x
Step 2: Combining like terms by adding the coefficients of x.
8x - 8 - 6x = (8x - 6x) - 8 = 2x - 8
Step 3: The simplified expression is 2x - 8. Thus, it is different from 3x.
Therefore, the student's claim that 8x - 2(4+3x) is equivalent to 3x is incorrect.