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Solving Linear Equations
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Sum of the Roots of a Quadratic
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Solving Equations 3
Solving Quadratic Equations
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Solving Linear Equations

Techniques for Solving Linear Equations

Writing down every step when solving an equation is not always necessary. Solving an equation is often part of a larger problem, and anything that we can do to make the process more efficient will make solving the entire problem fastar and easier. For example, we can combine some steps.

Combining Steps   Writing Every Step
4x - 5 = 23   4x - 5 = 23
4x = 28 Add 5 to each side. 4x - 5 + 5 = 23 + 5
x = 7 Divide each side by 4. 4x = 28
     
      x = 7

The same steps are used in each of the solutions. However, when 5 is added to each side in the solution on the left, only the result is written. When each side is divided by 4, only the result is written.

The equation -x = -5 says that the additive inverse of x is -5. Since the additive inverse of 5 is -5, we conclude that x is 5. So instead of multiplying each sideof -x = -5 by -1, we solve the equation as follows:

-x = -5  
x = 5 Additive inverse property

Sometimes it is simpler to isolate x on the right-hand side of the equation:

3x + 1 = 4x - 5  
6 = x Subtract 3x from each side and add 5 to each side.

You can rewrite 6 = x as x = 6 or leave it as is. Either way, 6 is the solution.

For some equations with fractions it is more efficient to multiply by a multiplicative inverse instead of multiplying by the LCD:

 
Multiply each side by the reciprocal of
x  
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