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(5-3a)-(-4a+6)=(8a+1)-3(2a+3)

2 min read Jun 16, 2024
(5-3a)-(-4a+6)=(8a+1)-3(2a+3)

Solving the Equation: (5-3a)-(-4a+6)=(8a+1)-3(2a+3)

This article will guide you through the steps of solving the equation (5-3a)-(-4a+6)=(8a+1)-3(2a+3). Let's break it down step by step:

1. Simplifying Both Sides

First, we need to simplify both sides of the equation by removing the parentheses.

  • Left Side:
    • Distribute the negative sign: (5 - 3a) + (4a - 6)
    • Combine like terms: a - 1
  • Right Side:
    • Distribute the -3: (8a + 1) - (6a + 9)
    • Combine like terms: 2a - 8

Now, the equation is simplified to: a - 1 = 2a - 8

2. Isolating the Variable

Next, we need to isolate the variable a on one side of the equation. We can achieve this by:

  • Subtracting a from both sides:

    • (a - 1) - a = (2a - 8) - a
    • This simplifies to: -1 = a - 8

  • Adding 8 to both sides:

    • (-1) + 8 = (a - 8) + 8
    • This simplifies to: 7 = a

3. Solution

Therefore, the solution to the equation (5-3a)-(-4a+6)=(8a+1)-3(2a+3) is a = 7.

4. Verification

To verify our solution, we can substitute a = 7 back into the original equation:

(5 - 3(7)) - (-4(7) + 6) = (8(7) + 1) - 3(2(7) + 3)

  • Simplifying both sides:
    • (-16) - (-22) = (57) - (48)
    • 6 = 9

Since both sides of the equation are equal after substituting a = 7, our solution is verified.

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