When there are unknowns on both sides of the equal sign, you have to make sure these end up on the same side of the equal sign to make it possible to solve them. It doesn’t matter which side you choose, but the most common is the left-hand side.

Example 1

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Solve the equation $3x-7-x=-5+5x+18$

$$3x-7-x=-5+5x+18$$ |

Add equal terms:

$${2x}{-7}={5x}{+13}$$ |

$${2x-5x}={13+7}$$ |

Add equal terms:

$$-3x=20$$ |

Get rid of the number in front of $x$:

$$\frac{\text{\u22123}x}{\text{\u22123}}=\frac{20}{-3}$$ |

Put the minus sign next to the fraction:

$$x=-\frac{20}{3}$$ |

Look at Example 1 above. First you tidy up the equation, so that terms containing $x$ are on one side, and terms containing only numbers are on the other side. Then you add the terms together. That makes it look solvable—and it’s a simple matter to clean up the rest.

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