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 Property of Equality for Addition - can add the same term to both sides of an equation. Property of Equality for Subtraction - can subtract the same term from both sides of an equation. Property of Equality for Multiplication - can multiply both sides of an equation by the same term. Property of Equality for Division - 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: Look for Distributive Property. Combine like terms on same side of equal sign 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 This is not true! 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