Algebra I: Section 3



CC MATH I STANDARDS UNIT 3

4.5 SOLVING TWO-STEP EQUATIONS: PART 1

WARM UP: Solve part (a) equations, and then use that to find part (b) answers.

|1a) [pic] |2a) [pic] |3a) [pic] |

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|1b) What is 3r? |2b) What is x – 2? |3b) What is u + 18? |

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|4a) [pic] |5a) [pic] |6a) [pic] |

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|4b) What is 2s? |5b) What is [pic]? |5b) What is [pic]? |

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INTRODUCTION TO SOLVING TWO-STEP STEP EQUATIONS:

Find numbers that answer the following questions:

1) What can you double and then add 5 to get 13?

2) What can you triple and then subtract by 7 to get -1?

3) You can triple and then subtract by 1 to get 29?

4) What can you double and then add -6 to get -16?

5) What can you double and then subtract from 9 to get 5?

6) What can you half and then add 9 to get 15?

SOLVING TWO-STEP EQUATIONS: Verbal explanation by fill in the blanks

#1) 7m – 17 = 60

Step One: What minus 17 equals 60?

[pic] – 17 = 60

Step Two: What times 7 equals previous answer?

7[pic] = [pic]

#2) –2n – 25 = 13

Step One: What minus 25 equals 13?

[pic] – 25 = 13

Step Two: What times -2 equals previous answer?

-2[pic]= [pic]

#3) 7 + 3x = 40

Step One: 7 plus what equals 40?

7 + [pic] = 40

Step Two: What times 3 equals previous answer?

3[pic] = [pic]

#4) 12 + 5y = 27

Step One: 12 plus what equals 27?

12 + [pic] = 27

Step Two: What times 5 equals previous answer?

5[pic]= [pic]

TWO-STEP EQUATIONS: Work Backwards

1) Find the VARIABLE.

2) Identify all operations.

3) In REVERSE ORDER of PEMDAS (SADMEP), cancel operations.

4) Use the same number and opposite operations

Operations: Operations: Operations: Operations:

1) 2y – 7 = 23 2) 8 + 6x = - 4 3) -5r - 18 = 12 4) 11 – 7x = 67

PRACTICE: SOLVING TWO-STEP EQUATIONS

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CC MATH I STANDARDS: UNIT 3

4.5 SOLVING TWO-STEP EQUATIONS: PART 2

WARM UP: Solve for the given variable.

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SOLVING 2-STEP EQUATIONS WITH FRACTIONS

• Solve in reverse order of operations = SADMEP

• FRACTIONS represent DIVISION statements.

• Be careful for hidden parentheses when there are OPERATIONS in numerator

|Option #1: |Option #2: |

|NO OPERATIONS IN NUMERATOR |OPERATIONS IN NUMERATOR |

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|[pic] |[pic] |

PRACTICE PROBLEMS

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WORD PROBLEMS INVOLVING MULTI-STEP EQUATIONS:

Write an equation for the problem below and then solve the equation.

|The product of negative 4 and y increased by 11 is equivalent to -5. |Eight more than five times a number is negative 62. |

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|8 less than twice a number is twelve. |The product of 5 and x decreased by 7 is as much as 42. |

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|How old am I if 400 reduced by 2 times my age is 244? |For a field trip 4 students rode in cars and the rest filled nine buses. How many |

| |students were in each bus if 472 students were on the trip? |

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|Sarah won 40 super bouncy balls playing horseshoes at her school's game night. |You bought a magazine for $5 and four erasers. You spent a total of $25. How much |

|Later, she gave two to each of her friends. She only has 8 remaining. How many |did each eraser cost? |

|friends does she have? | |

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|Two-thirds of a number minus six is –10 |One-fourth of a number increased by 5 is as much as 3. |

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|3 fifths of a number less than 9 equals 2 |11 minus one-half of a number is -13. |

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