0 5(x+1 6)+1 4(3x+2 4)=9 8

2 min read Jun 17, 2024
0 5(x+1 6)+1 4(3x+2 4)=9 8

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.

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