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.) = -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.) x = 18

• Ex:

Find an equivalent equation to - n = 5

6-4

• Solve two-step equations• STEPS:

1.) Upside down T2.) Add or subtract on both sides3.) Upside down T4.) Multiply or divide on both sides5.) 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 +

• How do we solve an equation that looks like this…

= 35

• Now solve this one…

92 =

• 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/subtract4.) Multiply/divide5.) Check back into original equation

• Exs: Solve and check.

1.) -4 – x – 3x = 8 2.) 3(x + 4) – 8 = -8

• Exs: Finding equivalent equationsSolve the following equations. Round to the nearest hundredth if necessary1.) -4(3x + 5 + 8x) = 7

• Exs: Finding equivalent equationsSolve the following equations. Round to the nearest hundredth if necessary2.) 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.) < -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 T2.) Add/subtract—bring sign straight down3.) Upside down T4.) Multiply/divide*If multiply/divide by a negative number, FLIP signAnswer: variable, inequality sign, #

• Exs: Solve and graph solution

1.) 5x – 7 ≥ 43 2.) 7 – > 12

• 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 sign4.) Multiply/divide*If you multiply/divide by negative #, FLIP SIGN5.) Graph solution

• Exs: Solve and graph1.) 7y – 3 – 10y < 12

2.) -32 ≥ 3(8 – 2n) – 2n