To solve the equation: 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
Step 1: To get from the original equation to this step, we distributed the 24 to both terms inside the parentheses.
Step 2: We subtracted 816 from both sides of the equation to isolate the term with variable x.
Step 3: We simplified by combining like terms on the left side of the equation.
Step 4: To solve for x, we divided both sides of the equation by 24.
To solve the equation 24(34+x)=1,200, the following steps were taken:
Step 1: Distribute the 24 on the left side of the equation:
24 * 34 + 24*x = 1,200
Reason: The distributive property allows us to multiply each term inside the parentheses by 24.
Step 2: Combine like terms on the left side of the equation:
816 + 24x = 1,200
Reason: The multiplication of 24 and 34 gives us 816, and we keep the 24x term as it is.
Step 3: Isolate the term with x by subtracting 816 from both sides of the equation:
816 - 816 + 24x = 1,200 - 816
Reason: To move the constant term to the other side of the equation, we subtract it from both sides. This maintains the equality of the equation.
Step 4: Simplify the equation:
24x = 384
Reason: Subtracting 816 from 816 cancels out that term on the left side, and subtracting 816 from 1,200 gives us 384 on the right side.
Step 5: Solve for x by dividing both sides of the equation by 24:
x = 16
Reason: Dividing by 24 on both sides isolates the variable x and gives us the solution.