Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Write the steps in solving 6n−4+5n=73.6n-4+5n=73. Justify each step with an appropriate property. (3 points)
To solve the equation 6n - 4 + 5n = 73, follow these steps:
Step 1: Combine like terms on the left side of the equation.
11n - 4 = 73 (combined like terms)
Justification: The property used here is the distributive property, which allows us to add the coefficients of the same variable (n) together.
Step 2: Add 4 to both sides of the equation.
11n - 4 + 4 = 73 + 4 (additive property of equality)
Justification: By adding 4 to both sides of the equation, we maintain the equality since the same value is added to both sides.
Step 3: Simplify both sides of the equation.
11n = 77
Justification: By simplifying each side, we can isolate the variable (n) on one side of the equation.
Step 4: Divide both sides by 11 to solve for n.
11n/11 = 77/11 (multiplicative property of equality)
Justification: Dividing both sides of the equation by 11 allows us to isolate n on one side of the equation.
Step 5: Simplify both sides of the equation.
n = 7
Justification: By simplifying, we find that n equals 7.
Therefore, the solution to the equation 6n - 4 + 5n = 73 is n = 7.