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Q: Why is it important to do the same things to both sides of an equation?

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If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.

An algebraic equation is a mathematical equation in which one or both sides is an algebraic expression.

The equation remains in 'balance'

Multiply both sides ofthe equation by the 'denominator' of the fraction.

Without an equality sign it is not an equation but if you mean 18+m = 27 then by deducting 18 from both sides of the equation m = 9

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If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.

An equation has two sides, and each of these sides is equal to the other.

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Equal quantities may be added to both sides of a linear equation.

In any equation, regardless of the number adding or subtracting, multiplying or dividing, you must do the same to both sides. This ensures you are not changing the equation. If only one side was done, then the original equation has been altered and is no longer the same as it began. Changing both sides with the same values keeps all things equal.

You can add or subtract any quantity on both sides of an equation, without changing the equation's solution set. Just make sure you add or subtract the same thing on both sides.

The equation remains in 'balance'

An algebraic equation is a mathematical equation in which one or both sides is an algebraic expression.

It follows from the multiplication property of equality. Dividing both sides of an equation by the same number (not by zero, of course) is the same as multiply both sides of the equation by the number's reciprocal. For example, dividing both sides of an equation by 2 is the same as multiplying both sides by 0.5.

That both sides of the equation must be equal

When in doubt always square both sides of the equation.

Yes because this keeps both sides of the equation in balance.

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