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Solving the Equation: 0.5(x - 3) = 0.6(4 + x) - 2.6
This article will guide you through the steps of solving the equation 0.5(x - 3) = 0.6(4 + x) - 2.6.
Step 1: Distribute
Begin by distributing the constants on both sides of the equation:
- Left side: 0.5 * x - 0.5 * 3 = 0.5x - 1.5
- Right side: 0.6 * 4 + 0.6 * x - 2.6 = 2.4 + 0.6x - 2.6
The equation now becomes: 0.5x - 1.5 = 2.4 + 0.6x - 2.6
Step 2: Combine Like Terms
Simplify both sides by combining the constant terms:
- Right side: 2.4 - 2.6 = -0.2
The equation now becomes: 0.5x - 1.5 = 0.6x - 0.2
Step 3: Isolate x
To isolate the variable x, subtract 0.5x from both sides of the equation:
- 0.5x - 0.5x - 1.5 = 0.6x - 0.5x - 0.2
This simplifies to: -1.5 = 0.1x - 0.2
Step 4: Solve for x
Add 0.2 to both sides of the equation:
- -1.5 + 0.2 = 0.1x - 0.2 + 0.2
This simplifies to: -1.3 = 0.1x
Finally, divide both sides by 0.1 to get the value of x:
- -1.3 / 0.1 = 0.1x / 0.1
Therefore, x = -13.
Conclusion
By following these steps, we have successfully solved the equation 0.5(x - 3) = 0.6(4 + x) - 2.6 and found that x = -13.