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. 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
x
5
= 18
6-4
• Solve two-step equations
• STEPS:
1.)
2.)
3.)
4.)
5.)
6.)
Upside down T
Add or subtract on both sides
Upside down T
Multiply or divide on both sides
Answer: Variable = # (variable can be on either side)
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. Round to the
nearest hundredth if necessary
1.) -4(3x + 5 + 8x) = 7
• 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 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:
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
1.) 5x – 7 ≥ 43
𝑥
6
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.
Interpret the solution. How many people can
Joann invite to her party?