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Solving the Equation: 0.6(x - 2) + 4.6 = 0.4(7 + x)
This article will guide you through the process of solving the equation 0.6(x - 2) + 4.6 = 0.4(7 + x) step by step.
1. Distribute
First, we distribute the constants on both sides of the equation:
- 0.6(x - 2) becomes 0.6x - 1.2
- 0.4(7 + x) becomes 2.8 + 0.4x
This gives us the equation: 0.6x - 1.2 + 4.6 = 2.8 + 0.4x
2. Combine Like Terms
Next, we combine the constant terms on each side of the equation:
- -1.2 + 4.6 = 3.4
The equation now becomes: 0.6x + 3.4 = 2.8 + 0.4x
3. Isolate the x Term
Now, we want to get all the x terms on one side of the equation and the constant terms on the other side.
- Subtract 0.4x from both sides: 0.6x + 3.4 - 0.4x = 2.8 + 0.4x - 0.4x
- This simplifies to: 0.2x + 3.4 = 2.8
4. Solve for x
Finally, we isolate the x term by subtracting 3.4 from both sides:
- 0.2x + 3.4 - 3.4 = 2.8 - 3.4
- This gives us 0.2x = -0.6
Now, divide both sides by 0.2 to solve for x:
- 0.2x / 0.2 = -0.6 / 0.2
- This results in x = -3
Conclusion
Therefore, the solution to the equation 0.6(x - 2) + 4.6 = 0.4(7 + x) is x = -3.