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Solving Multistep Equations with Fractions Solving Multistep Equations with Like Terms 8y + 2 – 3y = 17 Solve: = 10 Solve: 5x – 5 7 = 10 = 70 5x – 5 7 5x – 5 • Follow the order of operations in reverse when solving equations with more than one operation (multistep equations). • Goals of solving multistep equations: • Place the variables on one side of the equal sign and the numbers on the other side. • Have the number in front of the variable equal to one. • Place the variables on the same side. • The number in front of the variable must be equal to one. • Two inverse operations are needed to solve the equation above – subtraction & division. Solving Two-Step Equations Using Division Solving Equations with Variables on Both Sides Solving Two-Step Equations Using Multiplication 3 x + 8 = 23 3 x + 8 = 15 x = 5 – 8 – 8 4 groups of -3 = -12 5n + 3 = 28 x – 5 = 20 5n = 25 = 5n 5 – 3 – 3 – 2 – 2 – 3x – 3x 4 • • 4 7 • • 7 + 5 + 5 + 5 + 5 0 9 x Subtract 3 from both sides of the equation. Multiply both sides by 4. Multiply both sides by 7. Divide both sides of the equation by 5. Divide both sides by 5. 25 5 1 4 = 25 x 1 4 = n 5n + 3 = 28 5 5x 5 75 5 = = = x 15 y = x 3 6 = x 100 Solve: x – 5 = 20 Solve: 1 4 Add 5 to both sides. 8y + 2 – 3y = 17 5y + 2 = 17 Multiply both sides by 7. Combine like terms (8y – 3y). Combine like terms (8y – 3y). Subtract 2 from both sides. Subtract 2 from both sides. 5y + 2 = 15 Divide both sides by 5. 5y 5 15 5 = 5x – 7 = 3x + 5 5x – 7 = 3x + 5 2x – 7 = 5 Solve: + 7 + 7 2x – 7 = 12 Add 7 to both sides. 2x 2 12 2 = Subtract 3x from both sides. Divide both sides by 2. © Copyright NewPath Learning. All Rights Reserved. 93-4701 www.newpathlearning.com Multistep Equations

\|xiBAHBDy01675lz[ Solving Multistep Equations with Fractions Solving Multistep Equations with Like Terms 8y + 2 – 3y = 17 Solve: = 10 Solve: 5x – 5 7 = 10 = 70 5x – 5 7 5x – 5 7 5x • Follow the order of operations in reverse when solving equations with more than one operation (multistep equations). • Goals of solving multistep equations: • _________________________________________ _________________________________________ • _________________________________________ _________________________________________ • Place the variables on the same side. • The number in front of the variable must be equal to . Solving Two-Step Equations Using Division Solving Equations with Variables on Both Sides Solving Two-Step Equations Using Multiplication 3 x + 8 = 23 3 x + 8 = 15 x = 5 – 8 – 8 5n + 3 = 28 x – 5 = 20 = = – 2 – 2 4 • • 4 7 • • 7 + 5 + 5 Subtract 3 from both sides of the equation. Multiply both sides by 4. Multiply both sides by 7. Divide both sides of the equation by 5. Divide both sides by 5. 1 4 = 25 x 1 4 = n = = x = y x = x 100 5n + 3 = 28 Solve: x – 5 = 20 Solve: 1 4 Add 5 to both sides. 8y + 2 – 3y = 17 5y + 2 = 17 Combine like terms (8y – 3y). Subtract from both sides. 5y + 2 = 15 Divide both sides by 5. 5y = 5x – 7 = 3x + 5 2x – 7 = 5 5x – 7 = 3x + 5 Solve: 2x = Add 7 to both sides. 2x = Subtract 3x from both sides. Divide both sides by 2. Key Vocabulary Terms • equation • inverse operation • multistep equation • operation • order of operations • variable • Two inverse operations are needed to solve the equation above – subtra ction & . . = © Copyright NewPath Learning. All Rights Reserved. 93-4701 www.newpathlearning.com Multistep Equations