Unit 2 Review
1. Prove the following equations by using the properties of equality and properties of operations.
a.
Statements
Reasons
1. 3x + (x - 8) =12
1.1.Given
Given
2. 4x - 8 = 12
2.2.simplified
by addition
Associative Property
of addition
Addition property
of equality
3. 4x = 20
3.3. addition
property
of equality
Division property
of equality
4. x = 5
4.4.division
property
of equality
Statements
1. 6x + 14 = 12.8
2. 6x = -1.2
3. x = -.2
Reasons
1. Given
2. subtraction property of equality
3. division property of equality
2. Solve: 3x - 4 - 6x = 12 + 2x
-3x - 4 = 12 + 2x (combined like terms)
+3x
+3x
-4 = 12 + 5x
-12 -12
-16 = 5x
5 5
3. Solve: 6x - 3 + 3x = 60 + 2x
9x - 3 = 60 + 2x
-2x
-2x
7x - 3 = 60
+3 +3
7x = 63
7
7
x=9
-16
x=
5
4. Solve: 2x + 4 ( 3x - 5) - 2 = 98 - 6x
2x + 12x -20 - 2 = 98 -6x
14x - 22 = 98 - 6x
+6x
+6x
20x - 22 = 98
+22 +22
20x = 120
20
20
x=6
5. Solve: 12x - 5 ≤ 2x + 15
-2x
-2x
10x - 5 ≤ 15
+ 5 +5
10x ≤ 20
10
10
x≤2
6. Solve: 2a = 64
2a = 2•2•2•2•2•2
a=6
7. Solve: 55 = 4a - 9
+9
+9
64 = 4a
4•4•4 = 4a
3=a
8. Solve the following system:
Using Substitution method:
y+3=x
3x + 4y = 16
9. Solve the following system: 5x -2y = -13
2x + y = 11 (multiply by 2)
3(y + 3) + 4y = 16
3y + 9 + 4y = 16
7y + 9 = 16
7y = 7
y=1
Using Elimination method: 5x -2y = -13
4x + 2y = 22
9x
=9
x
=1
2x + y = 11
2(1) + y = 11
y=9
y+3=x
1+3=x
4 =x
Solution: (4, 1)
Solution: (1, 9)
10. Solve the following system by graphing: -x + 4y = 2 (line 1)
2x + y = 7 (line 2)
26 11
point of intersection:
,
9 9
(
)
1
Line 1: slope intercept form y =
4
1
x+
2
Line 2: slope intercept form y = -2x + 7
8
6
4
2
15
10
5
5
2
4
6
8
10
15
11. Graph the solution: 3x < 4y
4x - 5y ≤ 2
3
Line 1: in slope intercept form
y>
x
4
4
2
Line 2: in slope intercept form y ≥ x 5
5
8
y
6
4
2
15
10
5
5
2
4
6
8
10
15
12. x = Acme calculators
y = Zenith calculators
System of equations :
using elimination:
-9x - 9y = -270
12x + 9y = 280
3x
= 10
10
x=
x + y = 30
12x + 9y = 280
80
y=
3
13. System of equations :
3
8.00 + 0.25x = y
6.50 + 0.50x = y
6.50 + 0.50x = 8.00 + 0.25x
x=6
Micah will earn more after 18 months.
14. a. System of inequalities:
3
x + 3y ≤ 150
10
3
10
3
x+
x≥0
y≥0
5
y ≤ 60
350
300
250
200
150
100
50
600
500
400
300
200
100
100
200
300
400
500
600
50
100
150
200
250
300
350
15.
0.75x + 1.25y ≤ 7
8
6
4
2
15
10
5
5
2
4
6
8
10
15