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§ 2.4 Solving Linear Equations with a Variable on One Side of the Equation Equations with a Variable on One Side 1. 2. 3. 4. 5. 6. If the equation contains fractions, multiply both sides by the LCD to eliminate fractions. Use the distributive property to remove parentheses. Combine like terms on the same side of the equal sign. Use the addition property to obtain an equation in the form ax = b. Use the multiplication property to isolate the variable. Check the solution in the original equation. Angel, Elementary Algebra, 7ed 2 Solving Equations Example: Solve the equation 3(4 – x) + 5x = 9. 12 – 3x + 5x = 9 (Distributive property) 12 + 2x = 9 (Combine like terms.) 12 - 12 + 2x = 9 - 12 (Add –12 to both sides.) 2x = -3 (Divide both sides by 2.) x 3 2 Don’t forget to check! Angel, Elementary Algebra, 7ed 3 Solving Equations with Fractions Example: Solve the equation 45 n 13 . 15(4 n) 151 5 3 3 5 4 15( )15n 151 51 31 12 + 15n = 5 15n = -7 n = -7/15 (Multiply by the LCD, 15.) (Distribute.) (Simplify.) (Add –12 to both sides.) (Divide both sides by 15.) Angel, Elementary Algebra, 7ed 4 Helpful Hints and Definitions To evaluate an expression means to find its numerical value. To simplify an expression means to perform operations and combine like terms. To solve an equation means to find the value of the variable that makes the equation a true statement. Angel, Elementary Algebra, 7ed 5