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1.3 Solving Linear Equations

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-7x 2 +4x 3 d. 12x+3= -4x-8. Properties of Equality.

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1.3 Solving Linear Equations

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  1. 1.3 Solving Linear Equations p. 19

  2. 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

  3. 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!

  4. 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.

  5. Example: Solve for the variable.

  6. Ex: Solve for x.

  7. 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 Ex: Solve the equations.

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

  9. 1.4 Rewriting Equations & Formulas p. 26

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

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

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

  13. 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

  14. Assignment

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