More Equations Solving Multistep Equations

Some equations may have more than two steps to complete. You may have to simplify the equation first by combining like terms or even remove fractions to make solving easier. Samantha and Rebecca want to rent sports equipment at the city park. Samantha wants to rent inline skates, and Rebecca wants to rent a motor scooter. How would you write an equation and solve the problem to find the total cost for a specified number of hours. Let’s take a look at how you would solve this problem.

Here is the cost for each of the activities the girls would like to rent. Let’s look at each individually and then together. Inline Skates $3.00 plus $1.50/hour c = x c = individual cost x = number of hours rental Motor scooter $10.00 plus $2.75/hour c = x c = individual cost x = number of hours rental Independent variable Dependent variable constant Independent variable Dependent variable constant

Combined cost (C) Use the equation C = x x to answer each of the following questions. C = 4.25x + 13 How much would Samantha and Rebecca pay for 2 hours’ rental? How much would Samantha and Rebecca pay for 3 hours’ rental? If their total rental cost is $38.50, for how many hours did they use the equipment?

Multistep Equations Equations with Like Terms Equations that contain Fractions Equations with variables on both sides

Important! To solve multistep equations, first clear fractions and combine like terms. Then add or subtract variables to both sides so that the variable is on one side only. Multistep equations STEP 1: Clear fractions STEP 2: remove parenthesis STEP 3: move all variables to one side of the equation.

Solving equations containing like terms 8x x – 2 = 37 11x + 4 = 37 Combine like terms 11x + 4 – 4 = 37 – 4 Subtraction Property of Equality 11x = 33 Division Property of Equality x = 3 Remember to keep your equal signs lined up to prevent you from making a mistake. On the next slide we will check our answer by substituting for x.

Check your answer by substituting for x 8x x – 2 = 37 8(3) (3) – 2 = 37 Substitute 3 for x – 2 = 37 Combine like terms 37 = 37 ? True

Solve: 1) 8d – d + 2 = 13 2) 8x – 3x + 2 = -33 3) 2y + 5y + 4 = 25 4) 4x x -2x = 89 5) 30 = 7y – y

Solving equations that contain fractions 5n + 7 = -3 Multiply both side by 4 to clear fractions · 5n + 7 = -3 · 4 Multiply both sides by 4, Multiplication Property of Equality n + 7 = -3 Subtract 7 from both sides, Subtraction Property of Equality 5n + 7 – 7 = -3 – 7 5n = -10 Divide both sides by 5, Division Property of Equality 5 n = - 2 Remember to go back an substitute for n

Solve: 1) 4 – 2p = ) 9z + 1 = ) x + 2 =

Solving equations with variables on both sides is similar to solving an equation with a variable on only one side. You can add or subtract a term containing a variable on both sides of an equation. 2a + 3 = 3a 2a – 2a + 3 = 3a – 2a Subtract 2a from both sides. 3 = a Remember to keep equal (=) signs lined up to prevent errors. Always go back and check each equation by substituting the solution into the original equation. Moving terms is just like moving a single number, you use the Properties of Equality.

Solving equations with variables on both sides. 4x – 7 = 5 + 7x 4x – 4x -7 = 5 + 7x -4x Subtract 4x from both sides. -7 = 5 + 3x = 5 – 5 + 3x Subtract 5 from both sides. -12 = 3x -12 = 3x Divide both sides by = x Remember go back and substitute for x. Remember, you can move a whole term.

Solve: 1) 5x + 2 = x + 6 2) 4y – 2 = 6y + 6 3) 4(x - 5) + 2 = x + 3 4) 4x – 5 + 2x = x – 21 5) 8x – 3 = x

Both figures have the same perimeter. What is the perimeter. Remember how to find the perimeter of a polygon? Well, these two perimeters are the same.

Write an equation and solve the following problem. Sam and Ted have the same number of baseball trading cards in their collection. Sam has 6 complete sets plus 2 individual cards, and Ted has 3 complete sets plus 20 individual cards. How many cards are in a complete set? Find three consecutive whole numbers such that the sum of the first two numbers equals the third number. Hint: Let n represent the first number.)

Solve and check. 1)6x + 3x – x + 9 = 33 2)-9 = 5x x 3)4 – 2p = )y – 3y + 1 = )5y – 2 – 8y = 31 6)28 = 10a – 5a – 2 7)x + 2 = ) 5n – 2 – 8n = 31