To solve the equation: \large 3n+9+4n=2, give the reasons for each of the given steps. What was done to the previous step to get to the current equation? You can use the same reason more than once.
\large 7n+9=2
\large 7n+9-9=2-9
\large 7n=-7
\large n=-1
Word Bank:
Division as the inverse operation to isolate the variableAddition as the inverse operation to isolate the variableCombine Like TermsSubtraction as the inverse operation to isolate the variableMultiplication as the inverse operation to isolate the variableCombine Like Terms
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Blank 1: Subtraction as the inverse operation to isolate the variable
Blank 2: Division as the inverse operation to isolate the variable
Blank 3: Multiplication as the inverse operation to isolate the variable
Blank 4: Division as the inverse operation to isolate the variable
only the last one was correct.
\large 7n+9=2
Reason for each step:
\large 7n+9-9=2-9
Blank 1: Subtraction as the inverse operation to isolate the variable
Explanation: To isolate the variable term, we need to eliminate the constant term on the same side. By subtracting 9 from both sides of the equation, we can eliminate the constant term (+9) from the left side.
\large 7n=-7
Blank 2: Combine Like Terms
Explanation: By performing the subtraction on both sides, we simplify the equation by combining like terms on the left side. The variable terms (+7n) remain unchanged, and the constant terms (-9 + (-9)) combine to give -18.
\large n=-1
Blank 3: Division as the inverse operation to isolate the variable
Explanation: To solve for the variable n, we need to isolate it on one side of the equation. By dividing both sides by 7, we can cancel out the coefficient (7) on the left side and solve for n.
Blank 4: Division as the inverse operation to isolate the variable
Explanation: After simplifying the left side, we divide both sides by 7 to solve for n. Dividing -7 by 7 gives us -1.
Blank 1: Combine Like Terms
Reason: In the first step, we combined the like terms (3n and 4n) on the left side of the equation by adding them together. This step simplifies the equation and helps us isolate the variable.
Blank 2: Subtraction as the inverse operation to isolate the variable
Reason: In the second step, we subtracted 9 from both sides of the equation to isolate the variable term (7n). This step helps move the constant term (9) to the other side of the equation.
Blank 3: Combine Like Terms
Reason: In the third step, we combined the like terms (-9 and 2) on the right side of the equation by subtracting them. This step further simplifies the equation.
Blank 4: Division as the inverse operation to isolate the variable
Reason: In the final step, we divided both sides of the equation by 7 to solve for the variable (n). This step helps us isolate the variable and find its value.