To solve the equation: 24(34+x)=1,200
24
(
34
+
x
)
=
1
,
200
, give the reasons for each of the given steps.
What was done to the previous step to get to the current equation?
(1 point)
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Step 1: 816+24x=1,200
Step 2: 816−816+24x=1,200 − 816
Step 3: 24x=384
Step 4: x=16
Distributive property
Subtraction as the inverse operation to isolate the variable
Combine like terms
Addition as the inverse operation to isolate the variable
Multiplication as the inverse operation to isolate the variable
Division as the inverse operation to isolate the variable
Step 1: Distributive property - The equation is simplified by multiplying 24 with both terms inside the parentheses.
Step 2: Combine like terms - 816 and -816 cancel each other out, leaving 24x on one side of the equation and 1,200 - 816 on the other side.
Step 3: Subtraction as the inverse operation to isolate the variable - 816 is subtracted from both sides of the equation to isolate the 24x term.
Step 4: Division as the inverse operation to isolate the variable - The equation is divided by 24 on both sides to solve for x.
Step 1: Distributive property
In this step, the equation is multiplied by 24 using the distributive property to eliminate the parentheses. This is done to simplify the equation and isolate the variable.
Step 2: Subtraction as the inverse operation to isolate the variable
In this step, 816 is subtracted from both sides of the equation. This is done to isolate the term with the variable, 24x, on one side of the equation. By subtracting 816 from both sides, we get rid of the constant term on the right side.
Step 3: Combine like terms
In this step, 816 is subtracted from 1,200 to simplify the equation. This is done by combining like terms.
Step 4: Multiplication as the inverse operation to isolate the variable
In this step, the equation is divided by 24 to solve for x. This is done by using multiplication as the inverse operation of division to isolate the variable x on one side of the equation.
Therefore, the reason behind each step is as follows:
Step 1: Distributive property
Step 2: Subtraction as the inverse operation to isolate the variable
Step 3: Combine like terms
Step 4: Multiplication as the inverse operation to isolate the variable