Shortcut Moves: Moving Terms Across The Equals Sign

Use the shortcut where a term changes sign as it crosses '=', and know why it works.

4 micro-lessons

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Three Shortcut Rules

What appears on the other side when a term or factor leaves one side.

Doing the same thing to both sides removes a term or a factor from one side. We can write the result directly.

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The book's two ways of solving the same equations, side by side.

Problem. Compare the long way and the short way. (Textbook p. 173)

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Terms change sign; factors swap × and ÷.

Moving across the '=' sign

+ a \to - a - a \to + a \times a \to \div a \div a \to \times a

What each part means

+ a, - a

— a term added or subtracted on one side

\times a, \div a

— a factor or divisor of the whole side

When it works

Move a factor only when it multiplies or divides the whole side. Then check by putting the answer back into the original equation.

Example

3 x + 5 = 20 \Rightarrow 3 x = 20 - 5 = 15 \Rightarrow x = 15 \div 3 = 5

Pick the correct next step.

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3x + 5 = 20. The next step is…