Download ANSWERS to the UNIT 2 REVIEW

Algebra 1 – Unit 2 REVIEW
1). What is the solution to the equation 8x + 5(4x – 6) – 8 = 8x – 14?
MGSE9.A.REI.3
8𝑥 + 20𝑥 − 30 − 8 = 8𝑥 − 14 Distribute the 5
28𝑥 − 38 = 8𝑥 − 14 Combine like terms on the same side of the equals
28𝑥 = 8𝑥 + 24 Add 38 to both sides
20𝑥 = 24 Subtract 8x from both sides
𝒙 = 𝟏. 𝟐 Divide each side by 20
2). What is the solution to the inequality
4x
– 16 < 2x + 4?
7
MGSE9.A.REI.3
4𝑥
7
< 2𝑥 + 20 Add 16 to each side
4𝑥 < 14𝑥 + 140 Multiply 7 on each side  7(2x+20)
−10𝑥 < 140 Subtract 14x from each side
𝒙 > −𝟏𝟒𝟎 Divide each side by -10. Flip the sign because you divided by a
negative.
3). It costs $5 to have a tote bag monogrammed with up to 16 letters and $.50 for each additional
letter. A club has a budget of $9.00 maximum per tote bag. How many additional letters can the
club at most put on the tote without exceeding their budget?
MGSE9.A.REI.3
5 + .50𝑙 = 9 The first 16 letters cost $5 and each additional letter costs $.50
. 50𝑙 = 4 Subtract 5 from each side to solve for l
𝒍=𝟖
Divide each side by .50 to find out how many additional letters you
can have.
4). What is the solution to the system?
3x + 6y = 45
2x + y = 9
MGSE9.A.REI.6
3𝑥 + 6𝑦 = 45
Multiply the second equation by -6 if you are solving
−12𝑥 − 6𝑦 = −54
by elimination
−9𝑥 = −9 Add the two equations together
𝑥 = 1 Divide each side by -9
2(1) + 𝑦 = 9 Plug 1 in for x in one of the equations
2 + 𝑦 = 9 Subtract 2 from each side
𝒚 =7
(1,7)
3𝑥 + 6𝑦 = 45
If solving by substitution subtract 2x from each side in the second equation
𝑦 = −2𝑥 + 9
3𝑥 + 6(−2𝑥 + 9) = 45 plug the second equation in for y in the first equation
3𝑥 − 12𝑥 + 54 = 45 Distribute the 6
−9𝑥 + 54 = 45 Combine like terms on the same side of the equals
−9𝑥 = −9 Subtract 54 from each side
𝑥 = 1 Divide each side by -9
𝑦 = −2(1) + 9 Plug x=1 into the new equation you created
𝒚 = 𝟕 (1,7)
5). What is the solution to the system?
x + 4y = 3
-5x – 20y = -15
MGSE9.A.REI.6
5𝑥 + 20𝑦 = 15
Multiply the first equation by 5 if you are solving
−5𝑥 − 20𝑦 = −15
by elimination
0 = 0 Add the two equations together INFINITE SOLUTIONS
𝑋 = −4𝑦 + 3
If solving by substitution subtract 4y from each side in the first equation
−5𝑥 − 20𝑦 = −15
−5(−4𝑦 + 3) − 20𝑦 = −15 plug the first equation in for x in the second equation
20𝑦 − 15 − 20𝑦 = −15 Distribute the -5
−15 = −15 Combine like terms on the same side of the equals INFINITE SOLUTIONS
6). What is the solution to the system? -3x + 3y = 4
MGSE9.A.REI.6
-5x + 5y = 15
15𝑥 − 15𝑦 = −20
Multiply the first equation by 5 if you are solving
−15𝑥 + 15𝑦 = −45
by elimination
0 = −65 Add the two equations together NO SOLUTION
−3𝑥 + 3𝑦 = 4
If solving by substitution subtract 5x from each side in the second equation, then divide
𝑦 = 𝑥+3
everything by 5 in the second equation
−3𝑥 + 3(𝑥 + 3) = 4 plug the second equation in for y in the first equation
−3𝑥 + 3𝑥 + 9 = 4 Distribute the 3
9 = 4 Combine like terms on the same side of the equals NO SOLUTION
7). The sum of two numbers is 76. Nine less than four times the smaller is the same as the larger.
Find the two numbers.
MGSE9.A.REI.6
𝑥 + 𝑦 = 76 You can substitute because the second equations is already in y=
4𝑥 − 9 = 𝑦
𝑥 + 4𝑥 − 9 = 76
5𝑥 − 9 = 76
5𝑥 = 85
𝒙 = 𝟏𝟕
17 + 𝑦 = 76
𝒚 = 𝟓𝟗
8). In five years, twice Jenny’s age will be three more than Willow’s age. The sum of their ages
now is 26. How old is Willow?
MGSE9.A.REI.6
2(𝑗 + 5) + 3 = 𝑤 + 5 Set up the two equations first
𝑗 + 𝑤 = 26
2𝑗 + 10 + 3 = 𝑤 + 5
Distribute the 2
𝑗 + 𝑤 = 26
2𝑗 + 8 = 𝑤
Combine like terms
𝑗 + 𝑤 = 26
𝑗 + 2𝑗 + 8 = 26 Plug the first equation in the second equation for w
3𝑗 = 18 Combine like terms
𝒋 = 𝟔 Divide each side by 3
𝒘 = 𝟐𝟎 26 minus 6 is 20
9). Which graph represents the solution to the system? 2x + y = 6
𝑦 = −2𝑥 + 6 Make both equations in the
-x + 3y = 1
1
𝑦 = 3𝑥 + 1
form y=mx+b
D
MGSE9.A.REI.6
a.
b.
c.
d.
10). Describe the graph that represents the solutions of the inequality y < 8x - 15.
MGSE9.A.REI.6 C
≤ and ≥ mean all points that lie ____ AND on
a. All of the points that lie above
c. All of the points that lie below
the line y = 8x - 15.
the line y = 8x - 15.
b. All of the points that lie on and
d. All of the points that lie on and
above the line y = 8x - 15.
below the line y = 8x - 15.
11). Which graph represents the solution to the inequality 4x – y < 5 ?
MGSE9.A.REI.12
−𝑦 < −4𝑥 + 5
𝑦 > 4𝑥 − 5 C
a.
b.
c.
d.
12). Jenny manages two departments at a printer plant: one department assembles the printers
and one packages them for shipment. Jenny knows that it takes 0.25 hours to assemble each
inkjet printer and 2 hours to assemble each laser printer. She has allotted no more than 120 hours
for assembly. She also knows that it takes 0.25 hours to pack each inkjet printer and 0.5 hours to
pack each laser printer. She has allotted no more than 40 hours for packing. Write a system of
inequalities represents the time Jenny has for her staff to assemble and package the printers.
MGSE9.A.REI.12
. 25𝑖 + 2𝑙 ≤ 120
. 25𝑖 + .50𝑙 ≤ 40
13).
MGSE9–12.F.IF.2
hn
Find f(5).= -1
At x=5 what does y equal?
Algebra 1 – Unit 2 REVIEW ANSWERS
Name: ______________________________
Date: _____________
Period: ______
For each problem, you MUST SHOW EACH STEP in getting your solution.
Students will be awarded 0 points if the question is not answered or if the student's response does
not relate to the question being asked, 1 point for organized relevant information resulting in an
incorrect final answer or the correct answer only and 2 points for the correct answer with
supporting documentation.
1). Graph the solution to the following system of linear inequalities.
MGSE9.A.REI.12
3x – 4y ≤ 16
-3x
-3x
-4y ≤ -3x + 16
-4 -4 -4
−𝟑
y≥ 𝟒 𝒙−𝟒
4x + 3y < 9
-4x
-4x
3y < -4x + 9
3 3 3
−𝟒
y< 𝟑 𝒙+𝟑
2). A math teacher wants to buy 20 new scientific calculators for the classroom. Acme and
Zenith make two different types of calculators. Acme calculators cost $15 each. Zenith
calculators cost $12 each. The math teacher has $276 to spend. Write and solve a system of
equations to find how many of each calculator she can buy.
MGSE9.A.REI.6
𝐴 + 𝑍 = 20
A= -Z + 20
-15Z+300+12Z=276
-3Z = -24
15𝐴 + 12𝑍 = 276
15(-Z + 20) + 12Z = 276
-3Z + 300 = 276
Z = 8 A= 12
3). You have 18 coins that are all quarters and dimes. If you have a total of $2.55, how many of
each do you have?
MGSE9.A.REI.6
𝑞 + 𝑑 = 18
. 25𝑞 + .10𝑑 = 2.55
d= -q +18
.25q + .10(-q+18)=2.55
.25q - .10q + 1.80=2.55 .15q=.75
.15q + 1.80=2.55
q=5 d=13
Use the following functions to answer 4-7.
g(x)= 𝒙𝟐 + 𝟕
f(x)= 2x + 9
h(x)= -3x + 1
4. g(7)
𝑔(7) = 72 +7
𝑔(7) = 56
5. h(-15)
6. Find x if j(x) = -4
12
ℎ(−15) = −3(−15) + 1
−4 = 𝑥
ℎ(−15) = 46
𝑥 = −3
MGSE9–12.F.IF.2
j(x)=
𝟏𝟐
𝒙
7. Find x if f(x)= 51
51 = 2𝑥 + 9
𝑥 = 21