Solving the Equation: 5x/2 - x = x/10 - 21/5
In this article, we will solve the equation 5x/2 - x = x/10 - 21/5. This equation involves fractions and variables, and we will use algebraic methods to find the value of x.
Step 1: Simplify the Equation
The first step is to simplify the equation by combining like terms.
5x/2 - x = x/10 - 21/5
To combine the fractions, we need to find the least common multiple (LCM) of 2, 10, and 5, which is 10. We can then rewrite the equation as:
5x/2 = (5x - 2x)/10 - 21/5 5x/2 = 3x/10 - 21/5
Step 2: Cross-Multiply
Next, we can cross-multiply to eliminate the fractions.
(5x/2) × 10 = (3x/10 - 21/5) × 10 25x = 3x - 42
Step 3: Simplify and Isolate x
Now, we can simplify the equation by combining like terms.
25x = 3x - 42 25x - 3x = -42 22x = -42
Finally, we can isolate x by dividing both sides of the equation by 22.
x = -42/22 x = -21/11
Therefore, the value of x is -21/11.
Conclusion
In conclusion, we have successfully solved the equation 5x/2 - x = x/10 - 21/5 using algebraic methods. The value of x is -21/11.
