-1%2F4(x%2B5)%3D4.jpeg "1/3(5x+3)-1/4(x+5)=4")
Solving the Equation: 1/3(5x+3) - 1/4(x+5) = 4
In this article, we will solve the equation 1/3(5x+3) - 1/4(x+5) = 4 step by step.
Step 1: Simplify the Equation
First, let's simplify the equation by evaluating the expressions inside the parentheses:
1/3(5x + 3) = (5x + 3)/3 -1/4(x + 5) = -(x + 5)/4
So, the equation becomes:
(5x + 3)/3 - (x + 5)/4 = 4
Step 2: Find a Common Denominator
To add or subtract fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12. So, we'll multiply each fraction by the necessary factors to get a denominator of 12:
(5x + 3)/3 = (4(5x + 3))/12 -(x + 5)/4 = -(3(x + 5))/12
Now the equation becomes:
(4(5x + 3))/12 - (3(x + 5))/12 = 4
Step 3: Combine the Fractions
Combine the fractions by adding them:
(20x + 12 - 3x - 15)/12 = 4
Step 4: Simplify and Solve for x
Simplify the equation by combining like terms:
(17x - 3)/12 = 4
Multiply both sides by 12 to eliminate the fraction:
17x - 3 = 48
Add 3 to both sides:
17x = 51
Divide both sides by 17:
x = 51/17
x = 3
Conclusion
The solution to the equation 1/3(5x+3) - 1/4(x+5) = 4 is x = 3.
