Download One-Step Equations

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Date:
Note: Many problems in this packet will be completed together in class during
review time. Students are not expected to complete every single problem in the
packet. They should complete several problems from each page-- in addition to
studying the notes and past quizzes– in order to be fully prepared for test.
TOPICS COVERED ON “equations/ inequalities” TEST:
Modeling One and Two-Step Equations (Balance scale with algebra tiles)
Solving One and Two-Step Equations
Equation Word Problems
Solving One-Step Inequalities
Graphing One-Step Inequalities
NOTES SPACE/HELPFUL TIPS (to be filled out in class):
Draw tiles onto the below balance scales in order to model the following:
One-Step Equations:
1.
x + -2 = 3
2.
5 + x = -1
3.
x + (-6) = 2
4.
x – 7 = -1
6.
x – (-2) = -3
5.
x – (-3) = 6
Two-Step Equations:
7.
2x + 4 = -8
8.
3x + (-1) = 14
Solve the following addition/ subtraction one-step equations:
1)
x + 3 = -21
2)
4 + x = 16
3) x – 2 = -1
4)
x – (-4) = -30
5)
-12 + x = 28
6)
x – (-100) = 75
7)
x + 9 = -5
8)
-15 = -6 + x
9)
-4 = x – 24
Solve the following multiplication/ division one-step equations:
1)
3x = -21
2)
x = -8
4
4)
99 = 9x
5)
x = -7
-6
7)
3x = -21
8)
2 x = -4
5
3) -8x = 64
6)
3x=6
4
9)
64 = -8x
Solve the following two -step equations:
1)
5x + 4 = -21
2)
x + 2 = -8
4
3) -8x – 2 = 62
4)
1 + 9x = 73
5)
x – 8 = -2
-6
6)
7)
15 = 3x + 12
8)
2x -3= 5
5
9)
10)
18 = 4x + 6
11)
x -3= 6
11
12)
3x + 3 = 6
4
9 - 7x = 58
3 - 12x = 51
SITUATION
1) Last week Frank ran 4 more miles than
his dad. Frank ran 16 miles. How many
miles did his dad run?
2) What is the maximum amount of pop
rocks packages you can buy with $6.00 if
one package costs $0.75?
3) You would like to save $200 for vacation
spending money. You already have $30
in your savings account and you plan on
saving $10 per week. How many weeks
will it take you to save the money?
4) You purchase three school play tickets,
plus some concession goodies for $8.00.
If you spent a total of $23, how much
was each ticket?
5) You sold five times the amount of girl
scout cookie boxes that Sheila sold. If
you sold 80 boxes, how many did Sheila
sell?
6) Mrs. Dyson unpacks a box of Christmas
ornaments. She splits the ornaments
equally among herself and her three
family members. Then, she finds an
additional 2 ornaments that she keeps
for herself. If Mrs. Dyson ends up with a
total of 24 ornaments (counting the
extra two), how many ornaments were
in the original box?
7) 344 seventh- graders went on a field
trip to Washington D.C. 15 students
traveled by car and the rest were equally
split among 7 school busses. How many
students were on each bus?
EQUATION
ANSWER
Fill-in-the-Blanks:
1) When multiplying or ______________________________ by a negative number, we __________________________
the inequality symbol.
For the following inequalities, decide whether you would need to switch the direction of the sign.
Write “yes” or “no” in the blanks:
2) __________
x + -3 > 4
3) __________
2x ≤ -4
4) __________
x >4
-4
5) __________
-5x < 20
6) __________
32 – x ≥ 4
7) __________
x ≤4
9
Solve each inequality and circle ALL the numbers that makes the inequality true:
8)
9)
x + 5 > -2
-3x ≤ 33
10)
x – 7 < -2
11)
x ≥ -20
4
-6
-8
-7
0
7
-9
-11
-12
-9.5
11
12
-1
6
7
-9
5
4
2
-90
-5
-4
-81
-79.5
-80
Solve AND graph the following inequalities:
12)
x+9 >2
12)
-5 + x < 2
12)
-6x ≥ 30
1)
25 > 5x
12)
x ≤ 4
-2
12)
15 + x < 24
12)
x > 3
3
12)
-12x < 60
12)
x + 45 ≥ -47
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Which of following numbers is a
solution to the inequality?
5x > 45
A
8
B
9
C 10
D
13.
7
14.
Which of following numbers is a
solution to the inequality?
-2x > 40
A
-20
B
-19
C -21
D
20