%2B2-6%3D0-5(7%2Bx).jpeg "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).