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Intermediate Algebra Chapter     1    2   3   4   5   6   7   8   9   10   11
Elementary and Intermediate Algebra
Chapter 2: Linear Equations and Inequalities in One Variable
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Solve, ๐‘ฅ + 7 = 9
 
x = 2
 
x + 7 = 9
     -7   -7

x = 2
 
 
Solve, ๐‘ฅ โˆ’ 3 = โˆ’7
 
x = -4
 
๐‘ฅ โˆ’ 3 = โˆ’7
   +3    +3
x = -4
 
Solve, 2๐‘ฅ = 24
 
x = 12
 
 
2x = 24
2 / 2 = 24 / 2 = 12
x = 12
Solve 2x = 10
x = 15
 
x = 10 /
x = 15
Solve, 5๐‘ฅ + 15 = 35
 
x = 4
 
5๐‘ฅ + 15 = 35
        -15    -15
5x = 20
20 / 5 = 4
 
 
๐‘ฆ โˆ’ 3 = 1
 
y = 10
 
๐‘ฆ โˆ’ 3 = 1
       +3   +3
๐‘ฆ = 4
4 /  = 10
 
Solve: 3x + 12 = 5



3๐‘ฅ + 12 = 5
        -12
3x = --7
-7 / 3
x=
 
 
Solve: 3๐‘ฆ = 11๐‘ฆ + 40

y =     โˆ’5

3y = 11y + 40
         -11y
-8y = 40
40 / -8 = -5
Solve: 2(6๐‘ฆ โˆ’ 4) = 16
 
x = 2
 
2(6y โˆ’ 4) = 16
12y โ€“ 8 = 16
         +8   +8
12y = 24
24 / 12 = 2
 
5๐‘ฅ + 3(6๐‘ฅ โˆ’ 7) = 25
 
x = 2
 
5x + 18x โ€“ 21 = 25
5x + 18x = 23x
23x โ€“ 21 = 25
       +21    +21
23x = 46
46 / 23 = 2
 
 
The sum of 3 consecutive odd integers is 51. Find the integers.
 
15, 17, 19
 
x + x + 2 + x + 3 = 51
3x + 6 = 51
3x + (6 โ€“ 6) = (51 - 6)
3x = 45
45 / 3 = 15
The first odd integer = 15.
15 + 2 = 17
The second odd integer = 17.
17 + 2 = 19
The third odd integer = 19
15 + 17 + 19 = 51
 
 
One angle of a triangle measures 30ยฐ more than the second angle.
The measure of the third angle is three times the sum of the first two angles.
Find the measure of each angle.
 
7.5ยฐ, 37.5ยฐ, 135ยฐ
 
Let x = the measure of the second angle.
Let x + 30 = the measure of the first angle.
Let 3(x + x + 30) = the measure of the third angle
 
x + x + 30 + 3(2x + 30) = 180
2x + 30 + 6x + 90 = 180
8x + 120 = 180
8x = 60
 
x = 7.5ยฐ
x + 30 = 37.5ยฐ
6x + 90 = 135ยฐ
 
 
If 2x +1 = 5, what is the value of x?
 
x = 2
 
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If 2x โ€“ 4 = 5 โ€“ x, what is the value of x?
 
 x = 3
 
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If โ€ 2(x + 1) = 5, what is the value of โ€ x?
 
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If  x + 3 = 5, what is the value of x?
 
x = 4
 
 
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Intermediate Algebra Chapter     1    2   3   4   5   6   7   8   9   10   11


A black text on a white background Description automatically generated
 
x = -
 
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If -2(x โ€“ 5) = 1, what is the value of โ€x?
 
x =
 
 
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If 2x โ€“ 5y = 1 and x = 1, what is the value of y?
 
y = -1
 
A math equations with numbers Description automatically generated with medium confidence
 
Absolute value equations
 

 
3 and -2
 
 

 
x > 2

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What values of x satisfy the inequality -2x + 1 > 5?
 
x < -2
 
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Solve the equation -10x โ€“ 6 + 4x = -4x + 8.
 
-7
 
-10 + 4x = -6x
-6x โ€“ 6 + = -4x + 8
+4x  +6       +4x +6
-2x = 14
14 / -2 = -7
 
5(2x โ€“ 3) = x + 3
 
2
 
5(2x โ€“ 3) = x + 3
10x โ€“ 15 =   x  +  3
-1x   +15 = -1x + 15
9x = 18
18 / 9 = 2
 

 
-9
 
 

        -1       -1
 = 6
6 / -
 
 
x + 0.06x = 742
 
700
 
x + 0.06x = 742
1x + 0.06x = 1.06x
742 / 1.06 = 700
x = 700
 
The perimeter of a rectangle is 72 meters. If the width is 8 meters less than the length, then what is the width of the rectangle.
 
8 meters
 
P = 2L + 2W
72 = 2(3W + 4) + 2W
72 = (6W + 8) + 2W
72 = 8W + 8
64 = 8W
8 = W
 
What formula expresses the area of a triangle A as a function of its base b and height h?

A=1/2 bh
 
 
If the area of a triangle is 54 square inches and the base is 12 inches, then what is the height?
 
9 inches
 
54 =  ยท h ยท 12
54 = 6 ยท h
h = 54 / 6
h = 9
 
 
How many liters of 20% alcohol solution should Maria mix with 50 liters of a 60% alcohol solution to make a 30% alcohol solution?
 
150 liters
 
20% + 60% (50) = 30% (x + 50)
0.2x + 0.6 (50) = 0.3 (x + 50)
0.2x + 30 = 0.3 (x + 50)
0.2x + 30 = 0.3x + 15
-0.2x -15    -0.2x โ€“ 15
15 = 0.1x
15 / 0.1 =       150
Brandon gets a 40% discount on loose diamonds where he works.
The cost of the setting is $250. If he plans to spend at most $1450,
then what is the price range (list price) of the diamonds he can afford?
 
$2,000
 
1,450 โ€“ 250 = x โ€“ 0.4x
1,200 = 0.6x
1,200 / 0.6 = 2,000
 
 
If the degree measure of the smallest angle of the triangle is one-half of the degree measure of the second largest angle,
and one-third of the degree measure of the largest angle, then what is the degree measure of each angle.
 
30o, 60o, 90o
 
The smallest angle.
x + 2x + 3x = 180
6x = 180
180 / 6 = 30
 
The second largest angle.
30 ยท 2 = 60 (one-half of the degree measure of the second largest angle)
 
The largest angle.
30 ยท 3 = 90 (one-third of the degree measure of the largest angle)
2
Intermediate Algebra Chapter     1    2   3   4   5   6   7   8   9   10   11


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