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Part 1) Simplifying Multistep Expressions, Combining Like Terms
Simplify the following expressions:
45
(3 + 6) × 3
b.)
d.) (6  2  7)  (3  5) 2
e.) (4 − 1 + 8 ÷ 8) × 5
f.) (10 × 2) ÷ (1 + 1)
g.) n − 10 + 9n – 3
h.) −2x + 11 + 6x
i.) n + 4 − 9 − 5n
8(5−4)−3
c.)
8
×
5−1
a.) (5 + 16) ÷ 7 − 2
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j.) −4 + 7(1 − 3m)
k.) −5n + 3(6 + 7n)
l.) −2n − (9 − 10n)
m.) −9(6m − 3) + 6(1 + 4m)
n.) −10(1 − 9x) + 6(x − 10)
o.) −7(n + 3) − 8(1 + 8n)
p.){|3 − 3| − (−4)} × 5
q.) |2| + 6 + |−4|
r.)
s.) 6|1 − 1|
t.) −6(1 + |−1|) − (−6)
u.) |3(6)| − |6| + 6
|−2−3|
5
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Part 2) Solving Linear Equations and Absolute Value Equations
Solve the following equations:
a.) −20 = −4𝑥 − 6𝑥
b.) 6 = 1 − 2𝑛 + 5
c.) 8𝑥 − 2 = −9 + 7𝑥
d.) 𝑎 + 5 = −5𝑎 + 5
e.) − 1 = 5 𝑝 + 3𝑝 – 8
f.) −(7 − 4𝑥) = 9
g.) 5𝑛 + 34 = −2(1 − 7𝑛)
h.) −3(4𝑥 + 3) + 4(6𝑥 + 1) = 43
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i.) 𝑝 − 4 = −9 + 𝑝
j.) 1 = −3𝑟 + 2𝑟
l.) 7|𝑥| = −56
m.)
o.) −10|𝑥 + 2| = 20
p.) −5|3 + 4𝑘| = −115
|𝑎−5|
8
=5
k.) −(𝑟 − 1) = −3𝑟 + 2𝑟 + 1
𝑥
n.) |7| − 8 = −7
q.) 3 − |8𝑥 − 6| = 3
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Part 3) Solving Inequalities, Compound Inequalities, Absolute Value Inequalities
Solve the following inequalities, then graph the solution on the number line.
a) 𝑥 + 5 < 12
b) 7 + 𝑥 ≥ 15
c) −𝑥 − 8 > 3
d) 3𝑥 − 10 ≤ 23
e) −4𝑥 + 2 > 3𝑥 + 30
f)
g) −4(2𝑥 − 3) > 36
h) 7(𝑥 + 2) ≥ 5(2𝑥 − 8)
j) 𝑥 < 2 𝑜𝑟 𝑥 ≥ 6
k) 𝑥 > −4 𝑎𝑛𝑑 𝑥 ≤ 3
3(𝑥−4)
2
≤ −15
i) 11𝑥 + 3 + 2𝑥 < 3𝑥 − 56 − 1
l) 𝑥 < 0 𝑎𝑛𝑑 𝑥 > 5
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m) 2𝑥 > 6 𝑜𝑟 4𝑥 < 20
p) −2(𝑥 − 5) − 3𝑥 < 30 𝑜𝑟
n) 36 < 2𝑥 − 2 ≤ 50
1
𝑥
3
5
6
+ <
o) −5𝑥 + 7 < 17 𝑜𝑟 8𝑥 − 9 < −25
8
3
q) −8 ≤ 3𝑥 + 7 < 16
Write the inequality that represents the graph.
r)
s)
Solve the following absolute value inequalities. Then, graph the solution on the number line!
t) |𝑥| < 4
u) |2𝑥| > −5
v) |𝑥 − 3| ≤ 9
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w) 4|𝑥 + 11| − 8 ≥ 16
x) −5|3𝑥 − 12| + 2 > −43
2
y) |5 𝑥 + 10| < −1
Part 4) Writing Equations of Lines, Modeling Linear Equations
Find the slope given two points. 𝒎 =
a) (2, 10) 𝑎𝑛𝑑 (−3, 12)
𝒚𝟐 −𝒚𝟏
𝒙𝟐 −𝒙𝟏
b) (−7, 1) 𝑎𝑛𝑑 (4, −8)
c) (4, −3) 𝑎𝑛𝑑 (1, −3)
List the slope and the y-intercept for each line.
3
7
d) 𝑦 = 9𝑥 − 5
e) 𝑦 = − 𝑥 + 20
f) 3𝑥 + 4𝑦 = 12
g) 𝑦 = 10
h) 𝑥 = −5
i) 𝑦 − 5 = 2(𝑥 + 3)
Write the equation of the line in slope-intercept with the given information. y = mx + b
j) 𝑚 = −4 , 𝑏 = 7
1
k) slope of − 2 and y-intercept of −5
3
l) m = 2 and contains (−2, 4)
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Write the equation of the line in slope-intercept with the given information. y = mx + b
m) Through (3, 5) 𝑎𝑛𝑑 (1, 3)
n) Through (3, −5) 𝑎𝑛𝑑 ( 1, −9)
Part 5) Solving Systems by Graphing, Substitution and Elimination
SOLVE BY GRAPHING. Remember to list the point of intersection! Then state whether the solution is
consistent independent, consistent dependent, or inconsistent.
a)
b)
𝑥 + 3𝑦 = 15
2𝑥 + 6𝑦 = 36
_________
c)
d)
2𝑥 + 3𝑦 = 5
4𝑥 + 6𝑦 = 10
_________
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SOLVE BY SUBSTITUTION
e)
f)
g)
SOLVE BY ELIMINATION
h)
i)
j)
SET UP A SYSTEM OF EQUATIONS AND SOLVE BY METHOD OF YOUR CHOICE.
k) The admission fee at a small fair is$1.50 for children and $4.00 for adults. On a certain
day, 2200 people enter the fair and $5050 is collected. How many children and how many adults
attended?
l) There are two trails near Pam's house that she runs regularly, a short loop and a long loop. Last week,
she ran 1 short loop and 5 long loops, for a total of 31 miles. This week, she ran 3 short loops and 5 long
loops, covering a total of 33 miles. What is the length of each loop?
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PART 6) Real Word Applications of all concepts and Function Talk!
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