Maran Illustrated Effortless Algebra
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Produced by the award-winning maranGraphics Group, Maran Illustrated Effortless Algebra is a valuable resource to a wide range of readers-from people first being introduced to algebra to those studying for their SATs or GEDs. Maran Illustrated Effortless Algebra shows the reader the best way to perform each task, while the full-color examples and clear, step-by-step instructions walk the reader through each task from beginning to end. Thorough topic introductions and useful tips provide additional information and exercises to help enhance the readers' algebra experience. Maran Illustrated Effortless Algebra is packed with essential information for those who are learning algebra for the first time, and will provide more experienced readers with a refresher course on the basics and the opportunity to gain more advanced skills. Maran Illustrated Effortless Algebra will cost less than the price of one private tutoring session, and will provide years of valuable reference.
smallest denominator of the fractions can evenly divide into this new denominator If it new denominator, repeat steps 3 and 4, largest denominator by 3, and ~hen 4, and so on, until the smallest (ammon denominator. divIdes mto the new denominator. denominator is the bottom number in a fractlon. denominator. • If the smallest denominator of the fractions evenly divides into the largest denominator, you have found the least common denominator, which is the largest denominator. 50 4
= 9 you would subtract 7 from each side of the equals sign to cancel out the 7 originally found on the left side. In this example, we would have x + 7 - 7 9 - 7, which leaves an answer of x = 2. = Thankfully, equations are easy to check. All you have to do is take the value you determined for the variable, replace the variable in the original equation with the value you found and then work out the problem. If one side equals the other, you have correctly solved for the variable. Solving
variables. see page 36. For information on multiplying and dividing variables, see page 38. combined on the same side of the equals sign (=). • In this example, 6x + 8x equals '14 x. f::::= • ~\oct;C'& Tip ..-- ... --- What should I do if I end up wilh a negative variable? t -.- lI ... b-:.(;, . If you end up with a negative sign (-) in front of a variable, such as -y = 14, you = 34 4) x + 5 - 2x + 3 14x 14x - 3x = 22 + 3x = 22 + 3x = 22 llx = 22 llx 11 = 22 11 =2 x - 3x
the x variables and the subscripts. • You have finished multiplying the matrices. 135 Working Witt, Matrices Question 1. Determine the order of each of the following matrices. A= [1-4 8] 2 B= 10 -6 4-20] [o -1 0 0 Question 2. Add or subtract the following matrices, if possible, to determine the matrices A + B, A + C, C + D, B - A and D - B. c= 1 [ 2 1 -3 Question 3. If A is a 2 x 2 matrix, B is a 3 x 3 matrix, C is a 3 x 2 matrix and D is a 2 x 3 matrix, determine whether you
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