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Extra resources for Algebra I (Cliffs Quick Review)
Therefore, this problem may be rewritten as 3'7 4 8 Now, follow the same procedure as shown in Example 13. 2 3'7=3#Y 8=6 4 8 Y 4 7 7 1 Dividing mixed numbers To divide mixed numbers, first change them to improper fractions (see the section “Multiplying mixed numbers” earlier in the chapter). Then follow the rule for dividing fractions (see the “Dividing fractions” section earlier in the chapter). Example 15: Divide. 9 8 18 3 = 27 = 1 7 3 53 ' 2 23 = 18 20 5 ' 3 # 5 #Y 8 20 4 Notice that after you invert and have a multiplication of fractions problem, you may then cancel tops with bottoms when appropriate.
Example 6: Solve the system by graphing x=4+y x – 3y = 4 First, find three values for x and y that satisfy each equation. ) x=4+y x – 3y = 4 x y x y 4 0 1 -1 2 -2 4 0 5 1 7 1 Now graph the two lines on the coordinate plane, as shown in Figure 5-1. A graph of lines x = 4 + y and x − 3y = 4 indicating solution. y (0,0) x (4,0) 4 4 + y 3y = = x− x Figure 5-1 54 CliffsQuickReview Algebra I The point where the two lines cross (4, 0) is the solution of the system. If the lines are parallel, they do not intersect, and therefore, there is no solution to that system.
Sometimes you may have to use more than one step to solve for an unknown. Example 2: Solve for x. 3x + 4 = 19 Subtract 4 from both sides to get the 3x by itself on one side 3x + 4 = 19 - 4 -4 3x = 15 42 CliffsQuickReview Algebra I Then divide both sides by 3 to get x. 3x = 15 3 3 x=5 Remember that solving an equation is using opposite operations until the letter is on a side by itself (for addition, subtract; for multiplication, divide, and so forth). To check, substitute your answer into the original equation.