Strategy #9: Use Shortcuts to Simplify Equations And Inequalities
• Addition and Subtraction: Cross out common quantities that are being added or subtracted on both sides of an equation or inequality.
• Multiplication and Division: Cross out common quantities that are being multiplied on each side of the equation if you can be certain they don’t equal zero. Quantities that are being divided on both sides of an equation can also be crossed out. In the case of inequalities be sure the quantity being multiplied or divided is not negative.
• Rational Expression: If each side of an equation is a single rational expression (i.e. a fraction) with common denominators cross out the denominators.
• Powers: If each side of an equation is a single power with common bases cross out common bases and set the exponents equal to each other. If the bases are not the same, often the problem is set up to make them equal (What’s curious? Strategy #2)