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Study Guide
Chapter 2
Name: __________________
Date: _________
Period: ________
Prioritized Standards
4.0 Students simplify expressions before solving linear equations and inequalities in one
variable, such as 3(2x-5) + 4(x-2) = 12
5.0 Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for each step.
DP Content Competencies
M01 - Problem Solving: Solve mathematical problems.
DP Personal Competencies
P01 - Self-management: Take responsibility for changing personal behaviors or
acquiring skills that lead to both social and academic success.
Simplify the following expressions by combining like terms
1) 3x + 5 + x² + y + 3x² + 2
2) 2x² + 1 + xy + x² + 2xy + 5
3) 2 + x² + 3x + y² + 4y + xy
4) 3y + 2 + 2xy + 4x + y² + 4y + 1
5) 3y + 2y + y² + 5 + y
6) 3xy + 5x + 2 + 3y + x + 4
7) 4m + 2mn + m² + m + 3m²
8) 2x + 3x + 3 + 4x² + 10 + x
9) 4x + 4y² + y² + 9 + 10 + x + 3x
10) 2x² + 30 + 3x² + 4x² + 14 + x
11) 20 + 5xy + 4y² +10 + y² + xy
12) X + x – 3 + 4x² + 2x – x
13) 8x² + 3x – 13x² + 10x² - 25x- x
14) 2x² + xy + y² + x + 3 + x² + 3xy + 2
15) 3x² - 2x + 7 – 5x² + 3x – 2
16) y + 2x – 3 + 4x² + 3x – 5y
17) 2x – 6x² + 9 -1- x – 3x
18) 2y² + 30x – 5y² + 4x – 4y – y
19) -10 + 3xy – 3xy + y² + 10 - y²
20) X + 3x – 3 + 2x² + 8x – 5
21) 3y + 14y² - 6y² - 9y + 1 – y – 3y
22) 2y² + 30xy – 2y² + 4y – 4x
23) X- 0.2x
24) 3 + 7x – (2+ 9x)
25) 6 – (3x-4) + 7x -11
26) 3x² + 10 - y² + 4x – 8x² - 5y – 8 + y² + 3
Evaluate the expressions below for the given values of the variables
1) 6/x + 9 if x= 3
2) 8x – 3 + y if x=2 and y=1
3) 2xy if x=5 and y= -3
4) -4d + 3 if d= -1
5) K- m if k=4 and m= -10
6) t/w if t=6 and w= -3
7) x² + y² if x= 7 and y = 5
8) 6m + 2n² for m=7 and n=3
9) 5x/ - 2 for x= -18
10) (6x) ² - x/5 for x=10
11) (k- 3) (k + 2) for k= 1
12) 6x- (3y + 7) – xy for x= 5 and y=3
Use guess and check to solve the following problems.
1) A cable 84 meters long is cut into two pieces so that one piece is 18 meters longer
than the other. Find the length of each piece of cable.
2) Susan is buying three different colors of tile for the kitchen floor. She is buying
25 more red tiles than beige tiles, and three times as many navy-blue tiles as beige
tiles. If Susan buys 435 tiles altogether, how many tile of each color does she
buy?
3) The base of a rectangle is three centimeters more than twice the height. The
perimeter is 60 centimeters. Find the base and height of the rectangle
4) The number of students attending the fall play was 150 more than the number of
adults attending. Student tickets cost $3, and adult tickets cost $5. A total of
$4730 was collected. How many students attended the play?
5) Patricia is thinking of two numbers. When she adds them, she gets 40. When she
multiplies them she gets 351. Help her younger sister, Laura, figure out the
numbers.
6) Sue wants to save $87 for tickets to a rock concert. If she has $23 now and will
save $4 per week, how long will it take her to get enough money to buy the
tickets?
7) Mr. Brown can buy a 24-ounce bag of ferret food for $1.19, or she can buy a 36ounce bag for $2.89. Which is the better deal? Justify your conclusion.
8) Ralph and Alfonso are shooting marbles. Ralph has five more marbles than
Alfonso, and they have a total of 73 marbles. How many marbles does each of
them have?
Use your mental-math skills to compute the following percentages.
1) 100% of 832
2) 50% of 832
3) 25% of 832
4) 10% of 832
Compare expressions and determine with expression is greater
1)
2)
3)
4)
5)
6)
3x – (2- x) + 1 or
-5 + 4x + 4?
2x² - 2x + 6 – (-3x) or – (3 – 2x²) + 5 + 2x?
-1 + 6y -2 + 4x – 2y or x + 5y – (-2 + y ) + 3x – 6
5- (2y -4) – 2 or
-y – (1+ y) + 4
3xy + 9 – 4x – 7 + x or - 2x + 3xy – (x-2)
x + 1 – (1-2x) or 3 + x-1 – (x-4)
Simplify and solve each equation for x
1) 3x-7 =2
2) 1+ 2x –x = x -5 + x
3) 3 – 2x = 2x -5
4) 3 + 2x – (x+ 1) = 3x – 6
5) – (x+ 3 –x) = 2x -7
6) -4 + 2x + 2 = x + 1 + x
7) 2x – 5 = -1 + 5x + 2
8) –x + 2 = 4
9) 4x – 2 + x = 2x + 8 + 3x
10) 4y – 9 + y = 6
11) 9- (2-3y) = 6 + 2y – ( 5 + y)
12) 2- 2x – (4-x) = 2 - 3 – (x-2)
13) X + 1 – 2 – (-x + 3) = 6 – (1 – 1)
14) 2x -7 = -x + 2
15) -2 – 3x= x + 6
16) 3x – 1 – ( 1) = x – 3 – (5)
17) -3x + 7= x – 1
18) 1 + 2x – 3 = 4x -2
19) -3 + x = -2x + 6
20) - (x-3) = - 4x
21) 2 – (3x- 4) = 2x - 9
Ms. Garcia’s teams earned the following scores on a quiz:
15, 20, 19, 20, 16, 20, 14, 18, and 17.
What is the mean, median and mode of the scores?
Use proportional reasoning to solve the following problems
1) A typical small bag of colored candies has about 135 candies in it, 27 of which
are blue. At this rate, how many blue candies would you expect in a pile of 1000
colored candies?
2) Ten calculators cost $ 149.50. How much would 100 costs? 1000? 500?
3) Tickets to 50 home baseball games would cost $1137.50. How much would it cost
to get tickets for all 81 home games? How many games could you go to for $728?
Rewrite using the distributive property. Simplify where possible
1)
2)
3)
4)
5)
8 (3m + 4n)
½ (6r + 10s)
¾ (12x + 16y)
(14 + 7a) 1/7
a ( 3b + 7)
Rewrite using the distributive property. Simplify where possible
1)
2)
3)
4)
5)
8x + 8y
20m + 15n
20x + x
25x + 9x
12a + 16a
Simplify using the commutative and associative properties of multiplication
1)
2)
3)
4)
5)
6)
7)
-3bc (5m)
5xy (-2x) (-3y)
7a (-4ab) (2a)
a (-13b) (22ab)
–cd (5c) (-7cd)
-15a (4b) (2bc)
7x (-9xy) (-8y)
Solutions of Equations
1)
2)
3)
4)
5)
Solve:
16x + 42 -13x = 24
17x – 19 – 8x = 53
-17x -22 – 8x= 128
51x + 18- 29x= -114
45x -21-19x= -255
Translate Sentences to Equations, and then solve the equation
1)
2)
3)
4)
5)
The product of 6 times a number and fifteen is forty-two
If 5 times a number is decreased by 12, the difference is 9
The product of three times a number and twelve is twenty
If seven is subtracted from six times a number, the result is 10
The product of three times a number and twelve is twenty