0 8(x-2)+2 6=0 5(7+x)

2 min read Jun 17, 2024
0 8(x-2)+2 6=0 5(7+x)

Solving the Equation: 0.8(x-2) + 2.6 = 0.5(7+x)

This article will guide you through the steps of solving the linear equation: 0.8(x-2) + 2.6 = 0.5(7+x)

Step 1: Distribute

Begin by distributing the constants on both sides of the equation:

  • 0.8(x-2) becomes 0.8x - 1.6
  • 0.5(7+x) becomes 3.5 + 0.5x

This gives us the equation: 0.8x - 1.6 + 2.6 = 3.5 + 0.5x

Step 2: Combine Like Terms

Next, combine the constant terms on both sides of the equation:

  • -1.6 + 2.6 = 1
  • This simplifies the equation to: 0.8x + 1 = 3.5 + 0.5x

Step 3: Isolate the x Term

Now, isolate the x term by subtracting 0.5x from both sides:

  • 0.8x - 0.5x = 0.3x
  • 3.5 + 0.5x - 0.5x = 3.5
  • This leaves us with: 0.3x + 1 = 3.5

Step 4: Isolate x

Finally, isolate x by subtracting 1 from both sides and dividing by 0.3:

  • 0.3x + 1 - 1 = 3.5 - 1
  • 0.3x = 2.5
  • 0.3x / 0.3 = 2.5 / 0.3
  • x = 8.33 (approximately)

Solution

Therefore, the solution to the equation 0.8(x-2) + 2.6 = 0.5(7+x) is x = 8.33 (approximately).

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