Unit 4 Test Review Chapter 6 Packet Lessons

Unit 4 Test Review Chapter 6 Packet Lessons 1 -8 Chapter 8 Book Lesson 6

6 -1 & 6 -2 • Solve one-step equations – Do the opposite of what’s happening to the variable on both sides! – Check your answer back into the original equation – Watch your signs! – Doesn’t matter what side variable is on

• Ex: • El Rodeo School has 837 students. El Rodeo School has 78 more students than Hawthorne. How many students are there at Hawthorne School? Write an equation and then solve.

• At Costco, 32 cans of Coke cost a total of $8. 96. What is the cost per can? Write an equation and then solve.

6 -3 • Solve one-step equations with rational coefficients – If variable is being multiplied by a decimal—divide both sides by the decimal – If variable is being multiplied by a fraction— multiply both sides by the reciprocal – Check your answer back into the original equation

6 -4 • Solve two-step equations • STEPS: 1. ) Upside down T 2. ) Add or subtract on both sides 3. ) Upside down T 4. ) Multiply or divide on both sides 5. ) Answer: Variable = # (variable can be on either side) 6. ) Check answer back into original equation

• Write an equation to find the missing side lengths for the triangle below with a perimeter of 47 inches. – Solve to find the missing side lengths!

• Ex: • Lou’s cell phone plan costs $39 per month. Text messages cost an additional $. 15 each. If Lou’s cell phone bill last month totaled $55. 05, write and solve an equation to find the number of text messages he sent.

6 -5 • Multi-step equations – Has parentheses OR – Has like terms on one side OR – Has 3 or more terms on one side • *Can only start solving when you have 2 or less terms on one side and you have combined any like terms

• Multi-step Equations • STEPS: 1. ) Distribute if needed (keep, change, opp) 2. ) Add like terms on one side of equation if needed (keep, change, opp) 3. ) Add/subtract 4. ) Multiply/divide 5. ) Check back into original equation

• Exs: Solve and check. 1. ) -4 – x – 3 x = 8 2. ) 3(x + 4) – 8 = -8

• Solve the following equations. Round to the nearest hundredth if necessary 1. ) -4(3 x + 5 + 8 x) = 7

• Solve the following equations. Round to the nearest hundredth if necessary 2. ) 7 x – 3(5 x – 4) = -18

Writing Inequalities • Order: variable, inequality sign, number • Use key words in problem to figure out inequality sign

• Exs: – Her earnings were no more than $64 – A minimum number of 12 participants is required to hold a bike rally

6 -6 • Solve one-step addition and subtraction inequalities *Solve inequalities the same way as equations • When adding or subtracting, bring inequality sign straight down for answer • Answer: variable, inequality sign, # – *Variable must be on the left!

• Ex: Solve and graph solution 1. ) 17 < x + 5 2. ) n – 8 ≤ -3

• Ex: A hurricane has winds that are at least 74 miles per hour. Suppose a tropical storm has winds that are 42 miles per hour. Write and solve an inequality to find how much the winds must increase before the storm becomes a hurricane. Interpret the solution.

6 -7 • Solve one-step multiplication and division inequalities – If you multiply or divide by a positive number, bring inequality sign straight down. – *If you multiply or divide by a negative number, FLIP the inequality sign.

• Ex: • T-shirts cost $18 each at the local sports store. Coach George can spend at most $162 on Tshirts for the basketball team. Write an inequality to find the number of T-shirts Coach George can buy. Interpret the solution. – Can he buy a T-shirt for all 12 members of his team? Why or why not?

6 -8 • Solve 2 -step inequalities • STEPS: *Upside down T 1. ) Add/subtract—bring sign straight down *Upside down T 2. ) Multiply/divide *If multiply/divide by a negative number, FLIP sign Answer: variable, inequality sign, #

• Ex: Skate Land charges a $50 flat fee for a birthday party rental and $5 person. Joann has no more than $100 to spend on the birthday party. Write an inequality to represent the situation. Interpret the solution. How many people can Joann invite to her party?

Multi-step Inequalities • Solve multi-step inequalities – Has parentheses OR – Has like terms on one side OR – Has 3 or more terms on one side • *Can only start solving when you have combined any like terms and have 2 or less terms on variable side • *Make sure variable is on left or move it 1 st!

• Solve multi-step inequalities • STEPS: 1. ) Distribute if needed (keep, change, opp) 2. ) Add like terms on one side of equation if needed (keep, change, opp) 3. ) Add/subtract—bring down sign 4. ) Multiply/divide *If you multiply/divide by negative #, FLIP SIGN 5. ) Graph solution

• Exs: Solve and graph 1. ) 7 y – 3 – 10 y < 12 2. ) -32 ≥ 3(8 – 2 n) – 2 n