14-1/5(x-10)=2/5(25+x)

Suzhoumeite

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Jun 29, 2024

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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.