The expression 4[7+(w+5)] is manipulated to generate an equivalent expression. In which step, if any, does the first error occur?
4[7+(w+5)]
Step 1: 4[w+(7+5)] Apply the Associative Property of Addition and add.
Step 2: 4[w+12]
Step 3: 4⋅w+12 Apply the Distributive Property.(1 point)
Responses
Step 3
Step 3
Step 2
Step 2
Step 1
Step 1
no error
The first error in manipulating the expression 4[7+(w+5)] occurs in Step 3.
Let's go through the steps to see where the error happens:
Step 1: 4[w+(7+5)] - This step correctly applies the Associative Property of Addition and adds 7 and 5 to get 12 inside the parentheses.
Step 2: 4[w+12] - In this step, we have simplified the expression further by substituting the value of 7+5, which is 12, into the parentheses.
Step 3: 4⋅w+12 - This is where the error occurs. The expression inside the square brackets, [w+12], should be multiplied by 4 using the Distributive Property. However, the error here is that only the w term is being multiplied by 4, while the 12 is not being multiplied.
To correct this error, the expression should be written as 4(w+12) instead of 4⋅w+12.
Therefore, the first error occurs in Step 3.
The first error occurs in Step 3 when the Distributive Property is incorrectly applied.
Apologies for the incorrect response. The first error actually occurs in Step 1 when the Associative Property of Addition is incorrectly applied. The correct expression should be:
4(7 + w + 5)