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Solving the Equation: 0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8
This article will guide you through the process of solving the equation 0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8.
Step 1: Distribute
Begin by distributing the constants outside the parentheses:
- 0.5 * x = 0.5x
- 0.5 * 1.6 = 0.8
- 1.4 * 3x = 4.2x
- 1.4 * 2.4 = 3.36
Now the equation becomes:
0.5x + 0.8 + 4.2x + 3.36 = 9.8
Step 2: Combine Like Terms
Combine the 'x' terms and the constant terms on the left side of the equation:
- 0.5x + 4.2x = 4.7x
- 0.8 + 3.36 = 4.16
The equation now looks like this:
4.7x + 4.16 = 9.8
Step 3: Isolate the Variable
To isolate the 'x' term, subtract 4.16 from both sides of the equation:
4.7x + 4.16 - 4.16 = 9.8 - 4.16
This simplifies to:
4.7x = 5.64
Step 4: Solve for x
Finally, divide both sides of the equation by 4.7 to solve for 'x':
4.7x / 4.7 = 5.64 / 4.7
This gives us:
x = 1.2
Conclusion
Therefore, the solution to the equation 0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8 is x = 1.2.