1.3 Solving Linear Equations

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Presentation transcript:

1.3 Solving Linear Equations Algebra II

What is an equation? A statement in which 2 expressions are = Ex 1: 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.

Solve for the variable. Ex. 1a) 1b) Distr. Prop.

Solve for x. Ex. 2) Fractions in equation.

Solve the equations. Ex. 3a) 3b) 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. 4 Work problems It takes you 45 minutes to mow your lawn & it takes your brother 30 minutes to mow the lawn. How long does it take you to mow the lawn if you have 2 mowers & work together.

Assignment