ALGEBRAIC EQUATIONS What Are Algebraic Equations? Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. To solve an algebraic equation, inverse operations are used. Two-step equations involve two different mathematical operations that must be evaluated in order to solve the equation. Equations can be solved using addition, subtraction, multiplication and division. Most two-step equations involve either addition or subtraction with either multiplication or division. Some algebraic equations can contain variables on both sides of an equation. In this case, the variables and numbers need to be moved so there are only variables on one side and numbers on the other side before evaluating. How to use algebraic equations Algebraic equations written as words or word problems must be changed into the correct numbers or variables before solving. For example, what is the phrase, five times a number decreased by four is sixty-three, as a mathematical equation? Ex. Five times a number → 5x decreased by four → -4 is sixty-three → = 63 The equation is 5x - 4 = 63. Once the words or word problems have been changed to numbers, the equation can be evaluated. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
To evaluate two-step equations, inverse operations are used. With two-step equations, it is very important to isolate the variable before evaluating. Isolating the variable means to get the variable alone on one side of the equation. For example, evaluate 3x + 2 = 23. Ex. 3x + 2 = 23 → isolate the variable by subtracting 2 - 2 -2 3x = 21 → now solve for x 3 3 x = 7 In this equation, x = 7. If 3 was divided first and then 2 was subtracted, the result would be incorrect. Algebraic equations can also have variables on both sides of the equal sign. To solve for these equations, the variables must be on one side of the equal sign and the numbers must be on the other side of the equal sign. Then the equation can be evaluated. For example, solve for 3x - 3 = x + 7. Ex. First move the numbers over → 3x - 3 = x + 7 +3 +3 The equation now becomes → 3x = x + 10 Now move the variable over → -x -x 2x = 10 x = 10/2 = 5 The answer for this equation is 5. Answers of algebraic equations should be checked by plugging the answer for x in the original equation. In this case, (3)(5) -3 = 5 + 7 or 15 - 3 = 12 or 12 = 12. © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. What is the algebraic equation that means a number divided by four plus two is six? 2. Solve for x, 3x - 7 = 5 3. Solve for x, x/6 + 21 = 27 4. Solve for x, 9 - 5x = -31 5. Solve for x, 12 + x = 6 + 3x 6. Solve for x, 3x/4 = 8 + x © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.