Look at the example of solving linear equations with fractions and whole numbers. There is nothing hard to understand here.

Example.

Solve the equation

30 + 2x = | 2x | + 2 |
---|---|---|

3 |

Solution.

We are finding out a value of the unknown x that makes the equality true.

We collect all the terms containing the unknown x on the left-hand side and whole numbers on the right-hand side of the equation.

We transpose 2x/3 from the right side to the left side by changing its sign

30 + 2x - | 2x | = 2 |
---|---|---|

3 |

Then we transpose 30 from the left side to the right side by changing its sign

2x - | 2x | = 2 - 30 |
---|---|---|

3 |

Now all the terms containing x are on the left and all the whole numbers are on the right.

Simplify the equation

2x * 3 | - | 2x | = -28 |
---|---|---|---|

3 | 3 |

6x - 2x | = -28 |
---|---|

3 |

4x | = -28 |
---|---|

3 |

Multiply either side by 3

4x * 3 | = -28 * 3 |
---|---|

3 |

4x = -84 |

Divide both sides by 4 to obtain the unknown x on its own

4x ÷ 4 = -84 ÷ 4

x = -21

x = -21

So, the solution of the linear equation is x = -21.

Is this solution correct?

To check the solution, we put the value (-21) of the unknown x in the equation

30 + 2x = | 2x | + 2 |
---|---|---|

3 |

30 + 2 * (-21) = | 2 * (-21) | + 2 |
---|---|---|

3 |

30 - 42 = | -42 | + 2 |
---|---|---|

3 |

-12 = | -36 |
---|---|

3 |

-12 = -12 |

The both sides of the equation are equal. It means that our solution x = -21 is correct.