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How to Identify Multistep Equations Some equations can be solved in one or two steps Ex) 4x + 2 = 10 is a two-step equation Subtract 2 Divide both sides by 4 Ex) 2x – 5 = 15 is a two-step equation Add 5 Divide both sides by 2 Some equations can be solved in one step, and some require two. The equation 4x + 2 = 10 {four x plus two equals ten} is a two-step equation. Solving it requires first subtracting 2 from both sides and then dividing both sides by 4. Although this equation requires two steps to solve, there is only one unknown term (x). The equation 2x – 5 = 15 {two x minus five equals fifteen} is another example of a two-step equation. The variable x appears only once, and solving for this variable requires only two steps. This image shows a sliding block puzzle. There are many ways that the blocks can be scrambled, and solving this type of puzzle requires many steps. However, the process of solving sliding block puzzles can be learned quickly because they are always solved the same way. {play animation, read following sentence as animation begins}. Following a certain sequence of steps leads to the solution regardless of how the puzzle was scrambled. When you have multiple movements – you are solving a multi-step equation!

How to Identify Multistep Equations Multistep equation – an equation whose solution requires more than two steps 5x – 4 = 3x + 2 4(x – 2) = 12 Multistep equations can take different forms Like the sliding block puzzle, some equations require many steps in order to solve. A multistep equation is an equation whose solution requires more than two steps. One example is the equation 5x – 4 = 3x + 2 {five x minus four equals three x plus two}. Notice that although there is only one unknown (x), it is present on both sides of the equation. These two occurrences of the variable can be combined, but doing this requires extra steps. The equation 4(x – 2) = 12 {four times x minus two equals twelve} is another example of a multistep equation. In this example, the distributive property must be used in order to simplify the left side of the equation. As a result, this equation requires more than two steps to solve. Although multistep equations can take different forms, there are certain features that indicate when an equation requires multiple steps in order to solve. One is if the variable is present in two different terms. These terms could be on the same side of the equation, as in 6x – 2x = 8 + 4 {six x minus two x equals eight plus four}, but frequently they are on opposite sides, as in 5x – 4 = 3x + 2 {five x minus four equals two x plus two}. Another feature that can indicate a multistep equation is the presence of parentheses on either side of it, as in 4(x – 2) = 12 {four times x minus two equals twelve. Some characteristics that indicate that an equation may require more than two steps are listed. Characteristic Example Multiple variable or constant terms on the same side x + 2x + 3x – 1 = 3 + 20 Variable present on both sides 4x – 2 = 3x + 3 Parentheses present on either side 3(x + 2) = 21

Steps to Solve a Multistep Equation How to Solve Multistep Equations 4(x + 2) – 10 = 2(x + 4) 4x + 8 – 10 = 2x + 8 4x – 2 = 2x + 8 2x = 10 x = 5 Steps to Solve a Multistep Equation First step Complete any Distributive Property Second step Combine like terms (same side of equal sign) Third step Move all variables to one side and constants to the other side. (+ or -) Fourth step Solve for the variable Step 1 Step 2 Step 3 Solving this equation required only four basic steps. Although multistep equations can appear in many different forms, the same general set of steps is useful in solving many of them. After identifying the problem as a multistep equation, apply the following steps. First, simplify each side of the equation as much as possible by combining like terms and using the distributive property if necessary in order to remove parentheses. Second, eliminate the variable on one side of the equation. Third, eliminate the constant term on the side with the variable. Fourth, divide each side by the coefficient of the variable. Some multistep equations may not require every step. For example, if the variable has no coefficient after the second step is completed, then the fourth step is unnecessary. Step 4 Same general set of steps is useful in solving many multistep equations!

Steps to Solve a Multistep Equation Practice with Multistep Equations − 4(5h + 2) − 22 = −40 8m − 32 + 7m − 34 = 9 30 = −5(6n + 6) −13 = 5(1 + 4m) − 2m 8(1 + 5x) + 5 = 13 + 5x Steps to Solve a Multistep Equation First step Complete any Distributive Property Second step Combine like terms (same side of equal sign) Third step Move all variables to one side and constants to the other. (+ or -) Fourth step Solve for the variable

Practice Solving All Types of Equations −20 = −4x − 6x 8x − 2 = −9 + 7x 5p − 14 = 8p + 4 −8 = −(x + 4) 14 = −(p − 8) −18 − 6k = 6(1 + 3k) 2(4x − 3) − 8 = 4 + 2x −(1 + 7x) − 6(−7 − x) = 36 −(7 − 4x) = 9 −3(4x + 3) + 4(6x + 1) = 43 Pass out student worksheet of the problems above. Students should complete the problems by following the four steps. As they work through the problems, they should also fill in the step they completed.

Solve it correctly for a free homework pass! Closure Your teacher gave the following problem out to everyone in your class for a chance at a free homework pass: −5(1 − 5x) + 5(−8x − 2) = −4x − 8x Your best friend was absent for the lesson when your teacher went over how to solve multi-step equations. He FREAKED out and stated, “There is NO WAY I can solve that! It is too long!” Explain to your friend how he can solve any type of equation. Make sure you describe the steps he should take. Solve it correctly for a free homework pass!