Unit 4 Test Review Chapter 6 Lessons 1-8

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

Exs: Solve and check. 1.) x + 7 = -16 2.) y – 4 = -18 3.) -9x = -108 4.) 𝑛 6 = -7

Ex: Jenny had 43 brochures to give out at the local job fair. At the end of the fair, she had 17 brochures left. Write an equation that could be used to find the number of brochures she gave out.

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

Exs: Solve and check. 1.) 3.5x = 21 2.) 3 5 x = 18

Ex: Find an equivalent equation to - 2 3 n = 5

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

Exs: Solve and check. 1.) -3y – 5 = 10 2.) -7 = 2 + 𝑛 3

How do we solve an equation that looks like this… 𝑥+7 4 = 35

Now solve this one… 92 = 𝑥 −12 5

How would you write a two-step equation to find the missing side length for this rectangle with a perimeter of 30 centimeters? Solve it to find the missing side length! x 7

What about for this triangle? 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: On one snowy day, Joey shovels 12 driveways. For each driveway, he gets paid $5.00 plus $1.50 an hour from his dad. How much does he make shoveling for 6 hours?

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 – 3x = 8 2.) 3(x + 4) – 8 = -8

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

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

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.

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.

Exs: Solve and graph solution 1.) -3b ≥ -24 2.) 𝑥 12 < -3

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

6-8 Solve 2-step inequalities STEPS: 1.) Upside down T 2.) Add/subtract—bring sign straight down 3.) Upside down T 4.) Multiply/divide *If multiply/divide by a negative number, FLIP sign Answer: variable, inequality sign, #

Exs: Solve and graph solution

Ex: Skate Land charges a $50 flat fee for a birthday party rental and $5 per person. Joann has no more than $100 to spend on the birthday party. Write an inequality to represent the situation. 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 1st!

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.) 7y – 3 – 10y < 12 2.) -32 ≥ 3(8 – 2n) – 2n