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(x-3)-(x+2)+2(x-1)-5=0

2 min read Jun 17, 2024
(x-3)-(x+2)+2(x-1)-5=0

Solving the Equation: (x - 3) - (x + 2) + 2(x - 1) - 5 = 0

This article will guide you through the steps of solving the given linear equation: (x - 3) - (x + 2) + 2(x - 1) - 5 = 0.

Understanding the Equation

The equation is a linear equation because the highest power of the variable x is 1. The equation involves several terms with parentheses.

Solving the Equation

  1. Simplify the parentheses: First, distribute the negative sign in front of the second parenthesis and the 2 in front of the third parenthesis:

    (x - 3) - (x + 2) + 2(x - 1) - 5 = 0
x - 3 - x - 2 + 2x - 2 - 5 = 0

  2. Combine like terms: Combine all the x terms and all the constant terms:

    (x - x + 2x) + (-3 - 2 - 2 - 5) = 0 
2x - 12 = 0

  3. Isolate the variable: To isolate x, add 12 to both sides of the equation:

    2x - 12 + 12 = 0 + 12
2x = 12

  4. Solve for x: Divide both sides by 2 to get the value of x:

    2x / 2 = 12 / 2
x = 6

Conclusion

Therefore, the solution to the equation (x - 3) - (x + 2) + 2(x - 1) - 5 = 0 is x = 6. You can verify this by substituting x = 6 back into the original equation.

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