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?
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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 simplify the equation, we multiplied 24 by (34+x) on the left side to get 816+24x.
Step 2:
To isolate the term with x, we subtracted 816 from both sides of the equation.
Step 3:
By simplifying the equation, we determined that 816-816 equals 0, leaving us with 24x=384.
Step 4:
To solve for x, we divided both sides of the equation by 24. This step is necessary because we want to isolate x, so we divide both sides by the coefficient of x, which in this case is 24.
Therefore, x=16.
Step 1: 816 + 24x = 1,200
Reason: We distribute the 24 from outside the parentheses to both terms inside the parentheses.
Step 2: 816 - 816 + 24x = 1,200 - 816
Reason: We subtract 816 from both sides of the equation in order to isolate the term with the variable.
Step 3: 24x = 384
Reason: We simplify the equation by combining like terms on the left side of the equation.
Step 4: x = 16
Reason: We divide both sides of the equation by 24 to solve for x.