Solving the Equation: 1/4x + 2 - 1/3x = 1/2
In this article, we will solve the equation 1/4x + 2 - 1/3x = 1/2. This is a linear equation that involves fractions, and we will use simple algebraic steps to find the value of x.
Step 1: Combine like terms
First, let's combine the terms with the variable x:
1/4x - 1/3x = 1/2 - 2
To combine these terms, we need to find a common denominator, which is 12. So, we can rewrite the equation as:
(3x - 4x)/12 = -3/2
This simplifies to:
-x/12 = -3/2
Step 2: Multiply both sides by -12
To get rid of the fraction, we can multiply both sides of the equation by -12:
x = 18
Solution
Therefore, the value of x is 18.
We can plug this value back into the original equation to verify that it is correct:
1/4(18) + 2 - 1/3(18) = 1/2
Simplifying, we get:
4.5 + 2 - 6 = 1/2
0.5 = 1/2
Which is true!
So, the solution to the equation 1/4x + 2 - 1/3x = 1/2 is indeed x = 18.
