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SOLVING LINEAR EQUATIONS A RC I N STR UC TI ONAL V I DEO MAT 1 2 0 COL L EG E A LG EBR A Solving linear Equations A linear equation in one variable is an equation which can be written in the form: ax + b = c for a, b, and c real numbers with a 0. Linear equations with one variable: 2x + 3 = 11 2(x 1) = 8 can be rewritten 2x + (2) = 8 Example Solve: 4(x + 2) + 2 = 3x – 3(2x – 1) remove ( ) by applying distributive property 4x + 8 + 2 = 3x – 6x + 3 combine like terms on each side 4x + 10 = -3x + 3 transpose like terms to the same side (move terms so that all variable terms are on one side, and all number terms are on the other side Example (continue) REMEMBER!! When you move a term to the other side, you change the sign! 4x + 3x = 3 – 10 7x = -7 x = -7/7 x=-1 Example 2 2 x+5=x-7 3 2x+15=3x-21 -x=-6 x=6 -to clear the fraction you need to multiply each term by the LCD Solving absolute value equations Whenever you have: I I = positive number; in this case you will always have two solutions Example: I x-9 I = 15 Answer: X=-6, x=24 I I = 0; there will be one solution Example: I y-8 I = 0 Answer: y=8 I I= negative number; there is no solution Example: I z+7 I = -5 Answer: no solution