Solving the Equation: 14-1/5(x-10)=2/5(25+x)
In this article, we will solve the equation 14-1/5(x-10)=2/5(25+x). This equation involves fractions and variables, and we will use algebraic methods to solve for x.
Step 1: Simplify the Equation
First, let's simplify the equation by evaluating the expressions inside the parentheses:
14 - 1/5x + 2 = 2/5x + 10/5 + 2/5
Combine like terms:
14 - 1/5x + 2 = 2/5x + 12/5
Step 2: Isolate the Variable
Now, let's isolate the variable x by moving all the terms involving x to one side of the equation. We can do this by subtracting 2/5x from both sides:
14 - 1/5x - 2/5x = 12/5 - 2
Combine like terms:
14 - 3/5x = 12/5 - 2
Step 3: Solve for x
Next, let's solve for x by multiplying both sides of the equation by 5 to eliminate the fraction:
70 - 3x = 12 - 10
Simplify the equation:
70 - 3x = 2
Add 3x to both sides:
70 = 3x + 2
Subtract 2 from both sides:
68 = 3x
Divide both sides by 3:
x = 68/3
x = 22.67
Conclusion
Therefore, the solution to the equation 14-1/5(x-10)=2/5(25+x) is x = 22.67.