Name__________________________________________________Date___________Period_____
Unit 01 Test Review: Linear Expressions, Equations, and Inequalities
Solve each equation or inequality for the given
variable (graph the inequalities):
1.
15 − 3(−𝑥 + 5) = −21 + 6𝑥
2.
2(𝑥 − 1) + 𝑥 = 6 − (2𝑥 + 3)
6.
3(𝑥 + 8) ≥ 2(2𝑥 + 8)
7.
−9𝑥 − 3 + 8 > −3(3𝑥 + 5)
Write an inequality, solve and graph each problem.
3.
8.
Eight less than six times a number is less than five
times the number plus 21.
9.
The sum of twice a number and 5 is at most 3 less
than the number.
1
1
(3𝑑 − 2) = (𝑑 + 5)
8
4
4. −4𝑘 + 2(5𝑘 − 6) = −3𝑘 − 39
10.
5.
3𝑥 − 4 ≥ 6𝑥 + 11
Simplify the following expression:
2
5
5
1
(2𝑎 + 𝑏) − ( 𝑎 − 6𝑏) − ( 𝑎 + 𝑏)
3
12
6
6
11.
Simplify the following expression:
2.2(4.5𝑐 + 8𝑑) − (1.6𝑐 + 6.3𝑑) − 4(2.6𝑐 − 9.1𝑑)
16.
Bob’s Bowling Alley gives customers the first two
games for free. After the first two games, each
game costs $2.50.
Write an equation that represents c, the cost to play,
g, games at the bowling alley. How many games
could you play if you had $20?
12.
Lucy and Ethel are making chocolates on a
production line. Lucy’s production line moves at a
rate of 10 chocolates per minute, while Ethel’s
moves at a rate of 13 chocolates per minute.
Because Ethel arrives late to work, Lucy has
produced 42 chocolates before Ethel ever begins.
17.
In the equation 𝑦 = 8𝑥 + 2(𝑥 − 4), if 𝑦 = −2, then
what is the value of x?
18
The length of a rectangle “A” is 4 more than 3 times
its width. The length of rectangle “B” is 3 less than
four times its width. The widths of both rectangles
are the same.
a. Write an expression for each person to
represent the amount of chocolates they will
make.
b. After how many minutes will Ethel have
produced more chocolates than Lucy?
Part A: Write an expression to represent the
perimeter of rectangle “A”. Write an expression to
represent the perimeter of rectangle “B”.
13.
Solve for B:
1
𝐴 = 𝐵𝐶 + 15
4
Part B: If the perimeter of each rectangle is the
same, what would be the dimensions of each
rectangle?
14.
Solve for 𝑣𝑓 :
𝑣𝑓 − 𝑣𝑖
𝑎=
𝑡
19
Rectangle WXYZ has a length of 4x – 2 units and a
width of 6x + 9 units. Rectangle EFGH has a length
of 3x – 5 units and a width of 2x + 9 units.
Part A: Write an expression that can be used to
represent the sum of the perimeters of rectangles
WXYZ and EFGH.
15.
Solve for y:
3𝑥 + 8𝑦 = 32
Part B: Find the difference between the perimeters
of rectangles WXYZ and EFGH.