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Example 5-3c Objective Solve two-step equations

Example 5-3c Vocabulary Two-step equations Equations that have two different operations to solve the equation

Lesson 5 Contents Example 1Solve a Two-Step Equation Example 2Solve a Two-Step Equation

Example 5-1a Write the equation. 2y + 4 = -2 2y + 4 Ask “what is being done to the variable and coefficient?” 2y is being added by 4 Do the inverse on each side to “undo” the addition 1/2 Bring down 2y + 4 Subtract Bring down = - 2 = -2 Subtract 4 - 4

Example 5-1a 2y + 4 = -2 2y + 4 1/2 - 4 = Combine “like” terms Bring down 2y 2y + 0 Bring down = = Combine “like” terms -6 Use the Identity Property of Addition to add 2y + 0 2y = - 6 Ask “what is being done to the variable?” The variable is being multiplied by 2

Example 5-1a 2y + 4 = -2 2y + 4 1/2 - 4 = y + 0 = -6 2y = - 6 Do the inverse on each side to “undo” the multiplication Bring down 2y = - 6 2y = - 6 Using the fraction bar, divide both sides by Combine “like” terms 1 Bring down  y =  y = Combine “like” terms - 3 Use the Identity Property of Multiplication to multiply 1  y y = - 3 Answer:

Example 5-1b Answer: h = 2 1/2

Example 5-2a Write the equation. 4b - 2 Ask “what is being done to the variable and coefficient?” 4b is being subtracted by 2 4b - 2 = 6 Do the inverse on each side to “undo” the subtraction 2/2 Bring down 4b Add 2 Bring down = 6 = 6 Add 2 + 2

Example 5-2a 4b - 2 4b - 2 = 6 2/2 + 2 = Bring down 4b 4b Combine “like” terms + 0 Bring down = = Combine “like” terms 8 Use the Identity Property of Addition to add 4b + 0 4b = 8 Ask “what is being done to the variable The variable is being multiplied by 4

Example 5-2a 4b - 2 4b - 2 = 6 2/2 + 2 = b + 0 = 8 4b = 8 Do the inverse on each side to “undo” the multiplication Bring down 4b = 8 4b = 8 Using the fraction bar, divide both sides by Combine “like” terms 1 Bring down  b =  b = Combine “like” terms 2 Use the Identity Property of Multiplication to multiply 1  b b = 2 Answer:

Example 5-2b Answer: f = 4 2/2

End of Lesson 5 Assignment Lesson 9:5Solving Two-Step Equations All

Example 5-3a MOVIE NIGHT Three friends went to the movies. The tickets cost $6 each. They bought 2 large popcorns to share. If they spent a total of $24 at the movies, how much did a large popcorn cost? The cost of 2 large popcorns plus 3 tickets is $24. Two popcorns at $p each plus tickets costs $24 Words Variable Equation The cost of 2 large popcorns plus 3 tickets is $24. The cost of 2 large popcorns plus 3 tickets is $24 2p2p 3/3

Example 5-3b Solve equation Simplify. Answer: A large popcorn cost $3 2p = p + 0 = 6 Ask “what is being done to the variable?” First 2p is being added by 18 Do the inverse on each side to “undo” the addition 2p + 0 = 6 2p = 6 Next p is being multiplied by 2 Do the inverse on each side to “undo” the multiplication 1  p = 3 3/3

Example 5-3c SHOPPING Jen went to her favorite store at the mall. She bought 3 t-shirts which cost $12 each. She also bought 2 pairs of the same jeans. If Jen spent a total of $80 at the store, how much did each pair of jeans cost? Answer: $22 for each pair of jeans * 3(12) + 2x = 80 3/3