Final answer:
To solve for n in the given literal equation a (n − 2)+7=bn, distribute a, move terms, factor out n, divide, and check the answer.
Step-by-step explanation:
To solve for n in the given literal equation, we will apply the steps of algebraic simplification.
Step 1: Distribute the a to the terms inside the parentheses.
a(n - 2) + 7 = bn
an - 2a + 7 = bn
Step 2: Move all the terms containing n on one side of the equation.
an - bn = 2a - 7
Step 3: Factor out n from both terms.
n(a - b) = 2a - 7
Step 4: Solve for n by dividing both sides by the coefficient of n (a - b).
n = (2a - 7) / (a - b)
Check if the answer is reasonable by substituting the value of n back into the original equation.