1.3 Solving Linear Equations

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1.3 Solving Linear Equations p. 19

What is an equation? A statement in which 2 expressions are = Ex: Which of the following are equations? 3x-7=12 b. 24x+5 2x-7x2+4x3 d. 12x+3= -4x-8

Properties of Equality Addition prop of = - can add the same term to both sides of an equation. Subtraction prop of = - can subtract the same term from both sides of an equation. Multiplication prop of = - can multiply both sides of an equation by the same term. Division prop of = - can divide both sides of an equation by the same term. ** So basically, whatever you do to one side of an equation, you MUST do to the other!

To solve an equation for a variable: Do order of operations backwards (undo +/- first, then mult/div.) Keep going until the variable is by itself on one side of the equation You may have to simplify each side first.

Example: Solve for the variable.

Ex: Solve for x.

Ex: Solve the equations. 5(x-4)=5x+12 5x-20=5x+12 -20=12 Doesn’t make sense! Answer: No solution 7x+14 -3x=4x+14 4x+14=4x+14 0=0 This one makes sense, but there’s no variable left! Answer: All real numbers

Dry ice is solid CO2. It does not melt, but changes into a gas at -109 Dry ice is solid CO2. It does not melt, but changes into a gas at -109.3oF. What is this temperature in oC?

1.4 Rewriting Equations & Formulas p. 26

Examples Solve 11x-9y= -4 for y. Solve 7x-3y=8 for x. -11x -11x -9y=-11x-4 -9 -9 -9 Solve 7x-3y=8 for x. +3y +3y 7x=3y+8 7 7 7

Turn to page 28 in your book. Know the Common Formulas Chart on this page!

Ex: Solve the area of a trapezoid formula for b1. A = ½ (b1+b2) h 2A = (b1+b2) h

Last Example: You are selling 2 types of hats: baseball hats & visors. Write an equation that represents total revenue. Price of baseball cap # of caps sold # of visors sold Total Revenue Price of visor R = p1B + p2V

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