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: 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 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

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

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: 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 – 3x = 8 2.) 3(x + 4) – 8 = -8

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

Solve the following 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. 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.

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. 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: 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. Interpret the solution. How many people can Joann invite to her party?