(x-3)-2=6-2(x+1)

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x - 3) - 2 = 6 - 2(x + 1)

This article will guide you through the step-by-step process of solving the equation (x - 3) - 2 = 6 - 2(x + 1).

Step 1: Simplify both sides of the equation

• Left side:
  • Combine the constants: (x - 3) - 2 = x - 5
• Right side:
  • Distribute the -2: 6 - 2(x + 1) = 6 - 2x - 2
  • Combine the constants: 6 - 2x - 2 = 4 - 2x

Now, the equation looks like this: x - 5 = 4 - 2x

Step 2: Isolate the 'x' terms

• Add 2x to both sides: x - 5 + 2x = 4 - 2x + 2x
• Simplify: 3x - 5 = 4

Step 3: Isolate the 'x' term

• Add 5 to both sides: 3x - 5 + 5 = 4 + 5
• Simplify: 3x = 9

Step 4: Solve for 'x'

• Divide both sides by 3: 3x / 3 = 9 / 3
• Simplify: x = 3

Solution

Therefore, the solution to the equation (x - 3) - 2 = 6 - 2(x + 1) is x = 3.

Verification

To verify our answer, we can substitute x = 3 back into the original equation:

• (3 - 3) - 2 = 6 - 2(3 + 1)
• 0 - 2 = 6 - 2(4)
• -2 = 6 - 8
• -2 = -2

Since both sides of the equation are equal, our solution x = 3 is correct.