Solve the equation below. Choose the method you prefer to use.
n/3-5n/6 = 1/3
To solve the equation (n/3) - (5n/6) = 1/3, we can use the method of multiplying through by the least common denominator (LCD) to eliminate the fractions.
First, let's find the LCD of the fractions 3 and 6, which is 6.
Now, multiply every term in the equation by 6 to eliminate the fractions:
6 * (n/3) - 6 * (5n/6) = 6 * (1/3)
2n - 5n = 2
Simplifying the equation, we get:
-3n = 2
To solve for n, divide both sides of the equation by -3:
-3n / -3 = 2 / -3
n = -2/3
So, the solution to the equation n/3 - 5n/6 = 1/3 is n = -2/3.
To solve the equation (n/3) - (5n/6) = (1/3), we can follow these steps:
Step 1: Get rid of the denominators by multiplying every term in the equation by the least common multiple (LCM) of 3 and 6, which is 6.
6 * (n/3) - 6 * (5n/6) = 6 * (1/3)
2n - 5n = 2
Step 2: Combine like terms on the left side of the equation.
-3n = 2
Step 3: Solve for n by isolating the variable.
Divide both sides of the equation by -3 :
(-3n)/(-3) = 2/(-3)
n = -2/3
Therefore, the solution to the equation is n = -2/3.
To solve the equation (n/3) - (5n/6) = 1/3, we'll simplify the equation step by step using the preferred method of solving equations.
Step 1: Find the common denominator
The common denominator for the fractions involved is 6, so we multiply every term by 6 to eliminate the denominators:
(6 * n / 3) - (6 * 5n / 6) = (6 * 1 / 3)
Simplifying, we get:
2n - 5n = 2
Step 2: Combine like terms
Combine the terms on the left side of the equation:
-3n = 2
Step 3: Isolate the variable
To solve for n, we want to get n by itself on one side of the equation. Divide both sides by -3 to solve for n:
-3n / -3 = 2 / -3
Simplifying, we get:
n = -2/3
Therefore, the solution to the equation is n = -2/3.
Note: It's important to always double-check your solution by substituting it back into the original equation to ensure it satisfies the equation.