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# Algebraic Equations Topic

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ALGEBRAIC EQUATIONS What are algebraic equations? Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. Inverse operations are performing the opposite operation to what is being performed in the equation. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Multiplication and division are the inverse operations of each other. There are different types of algebraic equations. A one-step algebraic equation means that only one operation needs to be performed in order to solve the equation. A two-step algebraic equation means that two steps are needed in order to solve the equation. Another algebraic equation that is commonly used is the Interest equation, I = P · r · t. This equation is used to find simple interest, I, given the principle, P, the rate, r, and the time, t. When three of the four numbers are given, the fourth can be found using a two-step algebra. How to use algebraic equations: • Algebraic equations are solved using the inverse operations. To solve the equation n - 52 = 38, look to see what operation is being performed in the problem, subtraction. The inverse operation of subtraction is addition. The problem can be solved using the inverse operation of addition as the example shows: n - 52 = 38 + 52 +52 n = 90 Since 52 was subtracted in the initial problem, it will be added with inverse operations. The rule when dealing with equations is whatever is done to one side of the equation must be done to the other side. So © 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.

52 is added to 38 on the other side of the equal sign. When both sides are added, the 52's on the left side of the equation cancel out, leaving only the n. On the right side of the equation, 38 and 52 are added, giving the answer of 90. Therefore n = 90. This is a one-step equation. • Look at the two-step equation below and how to solve it. 3n + 12 = 27 - 12 -12 3n = 15 3 3 n = 5 In this equation, 12 is subtracted first from both sides. This because the variable needs to be alone before it can be solved. Now the equation is 3n = 15. Since the 3 is multiplied by n, division must be used in order to solve for n. When 3 is divided by both sides, the result is n = 5. T • The interest equation, I = P·r·t, is also a two-step equation. When given the principle, rate and interest, multiplication is used to solve for the interest. If interest is given, along with two others, use inverse operations to solve. © 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. Solve the following: n - 4 = 16 56 + n = 134 n + 98 = 207 2n - 6 = 12 4n - 36 = 144 5n + 75 = 110 2. Solve for I, I = P·r·t: P = $1000, r = 8%, t = 2 years P = $5000, r = 4%, t = 1 year 3. Solve for the missing variable, I = P·r·t: I = $500, r = 8%, t = 2 years I = $50, P = $2000, t = 1 year © 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.