To solve the equation: \large 24\left\langle34+r\right\rangle=1,200, give the reasons for each of the given steps. What was done to the previous step to get to the current equation?
\large 816+24r=1,200 Distributive Property
\large 816-816+24r=1,200-816 Subtraction as the inverse operation to isolate the variable
\large 24r=384
\large r=16
Word Bank:
Subtraction as the inverse operation to isolate the variableCombine Like TermsMultiplication as the inverse operation to isolate the variableDivision as the inverse operation to isolate the variableDistributive PropertyAddition as the inverse operation to isolate the variable
Blank 1:
Distributive Property
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Subtraction as the inverse operation to isolate the variable
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Blank 4:
Division as the inverse operation to isolate the variable
Blank 1: Subtraction as the inverse operation to isolate the variable
To get from the equation 816+24r=1,200 to 816-816+24r=1,200-816, the Distributive Property was used. The value inside the angle brackets, 34+r, was multiplied by 24 to distribute the 24 to both terms within the angle brackets. This resulted in the equation 816+24r=1,200.
Blank 2: Subtraction as the inverse operation to isolate the variable
To get from the equation 816+24r=1,200 to 816-816+24r=1,200-816, subtraction was used as the inverse operation to isolate the variable. Since the goal is to isolate the term with the variable, 24r, from the constant term, 816, a subtraction was performed. Subtracting 816 from both sides of the equation canceled out the 816 on the left side, leaving only 24r. Subtracting 816 from 1,200 on the right side of the equation resulted in 384.
Blank 3: Addition as the inverse operation to isolate the variable
To get from the equation 816-816+24r=1,200-816 to 24r=384, addition is not used as an inverse operation in this step. The equation does not involve addition, so there is no need for an inverse operation of addition.
Blank 4: Division as the inverse operation to isolate the variable
To get from the equation 24r=384 to r=16, division is used as the inverse operation to isolate the variable. Since the goal is to isolate the variable, r, from the coefficient of the variable, 24, division is performed. Dividing both sides of the equation by 24 results in r=16, which gives the solution to the equation.
Blank 1: Distributive Property
The Distributive Property is used to distribute the value outside the parentheses to the terms inside. In this step, the value 24 is distributed to both 34 and r.
Blank 2: Subtraction as the inverse operation to isolate the variable
To isolate the variable, we want to get rid of any terms that do not contain the variable. In this step, we subtract 816 from both sides of the equation to eliminate the constant term on the left side.
Blank 3: Addition as the inverse operation to isolate the variable
No operation is performed in this step. The equation is already simplified.
Blank 4: Division as the inverse operation to isolate the variable
To solve for the variable, we divide both sides of the equation by 24 in order to isolate the variable term and solve for its value. This step allows us to find the value of r.