Download Infinite Algebra 1 - Unit 1 Review: Solving Equations, Proportions

Algebra I
Name___________________________________
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Unit 1 Review: Solving Equations, Proportions, and Inequalities
Date________________
Solve each equation.
1) x - -5 = 11
2) 12 = 11 + k
{6}
3) 8b + 9 = 89
{1}
4) 10(8 + x) = 150
{10}
5) -9 - 4n + 2 - 3 = -4n + 5n
{7}
6) -5(1 + m) = -5 - 4m
{-2}
7) 16 = 4(-2 - 8 x) - 8( x + 2)
{0}
8) 8(3 x + 1) = 8( x + 7)
{-1}
{3}
Write an equation and then solve.
9) The membership fee for joining a gym is $60 a year. Members who want to take a dance class must pay
an additional $3 per class. Nonmembers have to pay $9 per class. After how many classes is the total
cost for members the same as the total cost for nonmembers?
60 + 3x = 9x; 10 classes
Worksheet by Kuta Software LLC
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Solve.
10) Ronnie has a bag of 300 M&M's; some are red and some are blue. If 100 of the M&M's are red, what is
ratio of blue M&M's to red M&M's?
2:1
11) What is the ratio of blue M&M's to total M&M's?
2:3
Solve each proportion.
12)
14)
8 r+2
5
2
9
2
=7
b
13) - =
{-1.55}
{-5.2}
6
n
=
4 3n + 10
15)
{-4.28}
5
7
=
v-5 v-1
{15}
Write and solve a proportion to find your answer.
16) At a local shelter, the ratio of dogs to cats is 3:5. If the shelter has 20 cats, how many dogs are there?
12 dogs
Worksheet by Kuta Software LLC
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Solve the literal equation for the variable indicated.
17) Solve d=rt for t.
18) Solve y = mx + b for m.
m = (y-b)/x
t=
d
r
Rewrite the equation in function form (solve for y).
19) 3x + y = 9
20) 5 + 10y = 20x - 5
y = 9 - 3x
y = 2x - 1
Solve each inequality and graph its solution.
21) 14 x < -168
-14
23)
-13
p
18
22) 4 - x < 5
-12
-11
-10
-9
-3
-2
18
17
18
19
20
-10
1
19
20
21
22
23
21
26) 5 ³ -6(3r - 7) - 1
25) -24 < 2 p + p
-12
0
24) -58 < -3 x + 2
- 3 > -2
16
-1
-8
-6
-4
-2
-1
0
1
2
3
4
5
6
7
Worksheet by Kuta Software LLC
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27) 20 - 2 x > - x + 8( x + 7)
-8
-7
-6
-5
-4
-3
28) -39 £ -4(-6 - 6n) + 3(7 + 6n)
-2
-1
-4
-3
-2
-1
0
29) r + 5r £ -6(r + 3) + 2(5r - 1)
-14
-13
-12
-11
-10
-9
-8
Solve each compound inequality and graph its solution.
30) -8 < a - 2 < -5
-8
-7
-6
-5
31) 6 < 5 + p < 10
-4
-3
-2
-1
0
32) -14 < 10 - 4 x < -2
0
1
2
3
4
5
-2
-1
0
1
2
3
4
5
6
33) -36 < 4k + 4 < 40
6
7
8
9
-12
-8
-4
0
4
8
Write an inequality and then solve to find the answer.
34) You are supplying chips for the neighboorhood football party. Each bag of chips costs $4. If you
cannot spend more than $25, what are the possible numbers of bags of chips you can buy?
4x <= 25; Up to 6 bags
Worksheet by Kuta Software LLC
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Write an inequality and then solve to find the answer.
35) You want to buy a pair of sneakers at a shoe store, and you can spend at most $80. You have a coupon
for $10 any pair of shoes at the store. What are the possible original prices of sneakers you can afford?
x-10<=80; Up to $90
Fill in the blank with "Always", "Sometimes", or "Never"
36) The sum of a rational number and an irrational
number is _________________ an irrational
number.
Always
37) The product of two rational numbers is
_________________ an irrational number.
Never
38) A whole number is _____________________
a rational number.
39) An integer is ___________________ an
irrational number.
Never
40) A real number is ___________________ a
rational number.
Sometimes
Always
41) An irrational number is ________________ a
whole number.
Never
Worksheet by Kuta Software LLC
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