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Keys to Remember: Solving Multi-Step Equations Therefore, each book cost \$20 before the coupon was applied. Now, simply solve for c like any other multi-step equation: 3(c) - 3(5) = 45 Then we applied the \$5 coupon to each book, and finally, we will multiply the cost of each book after the coupon by 3. Since each book costs the same amount, we denote this amount by the variable, c. How much did each book cost, c, before the coupon was applied?įirst, let’s set up an equation that models the situation: He ends up buying three books that all cost the same amount of money. The coupon is allowed to be used as many times as Sam wants. Therefore, the breakeven point for Distributor A and Distributor B would be 15 pounds.Įxample 2 Sam goes to a bookstore with a coupon for \$5 off a book. To check you answer, you can simplify substitute 15 into the variable to see if the equation is true: 5p + 10 = 2p + 1p + 40 What amount of pounds, p, would be a breakeven point for the two companies?įirst, let’s create an equation for the situation: 5p + 10 = 2p + 1p + 40 Distributor B sells their beans for \$2 a pound, plus \$1 per pound for shipping, plus a \$40 processing fee. Distributor A sells their beans for \$5 a pound, plus a flat \$10 shipping fee. Return to the Table of Contents Multi-step equation word problems Example 1 Rob owns a coffee shop and is looking at finding a new coffee distributor for his beans. To check you answer, you can simplify substitute -9 into the variable to see if the equation is true: 3(m + 3) - 4 = 2(m - 2) Solve for m in the following equation: 3(m + 3) - 4 = 2(m - 2) To check you answer, you can substitute 3 into the variable to see if the equation is true: 2(3z - 4) = 10 Solve for z in the following equation: 2(3z - 4) = 10 Return to the Table of Contents Multi-step equations with distributive property Example 1 Therefore, y = 9 is the correct solution. Simplified equation (all terms multiplied by 12 ) In order to solve equations, we use inverse operations to help us isolate the variable. Remember, an equation is solved when we have isolated the variable and found a value that makes the equation true. Return to the Table of Contents How to solve multi-step equations Here are some examples of multi-step equations: Never fear! We’re going to show you many examples of multi-step equations and how to solve these important aspects of Algebra 1. Some can be very simple, while others become more complex. Multi-step equations are a wide-ranging category of equations. So get your mathematical toolbox out! You never know what you might see in a multi-step equation! We also might have to combine like terms or use the distributive property to properly solve our equations. These problems can have a mix of addition, subtraction, multiplication, or division. A multi-step equation is an equation that takes two or more steps to solve. Now we are moving to multi-step equations. (Check out those links if you need a quick refresher!) We began our study of solving equations with one-step equations, then we moved on to two-step equations. Remember, an equation is a mathematical sentence that uses an equal sign, =, to show that two expressions are equal.
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