Solves the Equation: 5x - 1/10 + 2x + 3/6 = x - 8/15 - x/30
In this article, we will solve the equation 5x - 1/10 + 2x + 3/6 = x - 8/15 - x/30. This equation may seem complex at first, but we can simplify it step by step to find the value of x.
Step 1: Simplify the Fractions
Let's start by simplifying the fractions in the equation:
- 1/10 = 0.1
- 3/6 = 0.5
- 8/15 = 0.53 (approximately)
- x/30 = x/30 (we can't simplify this one further)
So, the equation becomes:
5x - 0.1 + 2x + 0.5 = x - 0.53 - x/30
Step 2: Combine Like Terms
Now, let's combine the like terms:
- 5x + 2x = 7x (combine the x terms)
- -0.1 + 0.5 = 0.4 (combine the constants)
The equation becomes:
7x + 0.4 = x - 0.53 - x/30
Step 3: Rearrange the Equation
Next, let's rearrange the equation to get all the x terms on one side and the constants on the other side:
7x - x = -0.53 - 0.4 - x/30
This simplifies to:
6x = -0.93 - x/30
Step 4: Solve for x
Now, let's solve for x:
6x = -0.93 - x/30
Multiply both sides by 30 to eliminate the fraction:
180x = -27.9 - x
Rearrange the equation to get:
181x = -27.9
Divide both sides by 181:
x = -27.9 / 181
x ≈ -0.154
Therefore, the value of x is approximately -0.154.
Conclusion
In this article, we have successfully solved the equation 5x - 1/10 + 2x + 3/6 = x - 8/15 - x/30. By simplifying the fractions, combining like terms, rearranging the equation, and solving for x, we found that the value of x is approximately -0.154.
