Linear equations

Linear equations are expressions that can reduce to the form ax+b=0, with a≠0. Their only solution is x=-(b/a) and the unknown x only appears raised to 1.

Examples linear equations:

linear equations
linear equation

Examples of nonlinear equations:



Equivalent equations

Two equations are equivalent if they have the same solution or both have no solution. Thus, the equations 5x–9=51 and 3x-7=89–5x are equivalent because the solution of both is x=12.
To solve an equation, we have to clear the x using a series of steps. Each step consists of transforming the equation into another equivalent equation, in which the x is closest to being cleared.

How to solve linear equations

Keep in mind the following rules to avoid making mistakes:

  • Add or subtract the same expression in the two members of the equality. That is, what is adding in one member passes by subtracting the other member, and vice versa.
  • Multiply or divide the two members by the same non-zero number. In other words, what is multiplying everything else from one member happens dividing the other, and vice versa.

How to solve a linear equation:

  1. Remove denominators, if any.

    For this, the two members of the equation are multiplied by a common multiple of the denominators; preferably, their least common multiple:
    how to solve a linear equation

  2. Remove parentheses, if any.

  3. Pass the x terms to one member and the numbers to the other member:

  4. Simplify each member:

  5. Clear the x and get the solution like this:

  6. Check by substituting the x for the solution obtained.

    Since they match, the solution is correct:

The best way to learn to solve linear equations is to practice doing lots of exercises. Start now and test yourself!

Linear equation exercises

1. Find out the value of x:

Ejercicios de ecuaciones

2. Solve the following equations:

Ejercicios de ecuaciones

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