Download Review for Solving Equations and Inequalities Retest Solve each equa

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Review for Solving Equations and Inequalities Retest
Solve each equation. Show your work! Leave all answers as integers or fractions.
1. x + (-9) = 13
2. 5 – 2x = 3x + 8
x = 22
x=-
3. ⅔(18x – 21) = 7 – 3(x – 3)
4. 5(2 – x) + 7x = -3(x + 5)
x=
5.
x = -5
(
)
6. x = -36
no solution
x = - 45
7.
8.
y = -11
x = -35
9.
10. ⅔(9x – 6) = 10x – 4(x + 1)
+ 5 = -2
x = 28
All Real numbers
Solve each inequality. Show your work!
Leave all answers as integers or fractions.
11.
-4
12.
x<8
13.
-7
x > - 35
x < -39
14. - 3x > 27
x < -65
15. 2(x + 6) < 2x + 2
x<-9
16. -3(x +2) < -3x +10
12 < 2
No Solution
17. 8y – 5 > -6y + 1
- 6 < 10
All Real Numbers
18. 8 - 8x < 40
y>
x>-4
19. 8(x – 1) > -8 + 8x
20. -3(2x – 1)
-8 >-8
No Solution
x > -1
1 – 8x
Solve The Following Compound Inequalities. Graph their Solutions.
21.
-6<k<1
-6
1
22.
v > 2 or v < 1
1
2
23. 40 < 5p – 10 or 3p + 6 < 42
p > 10 or p < 12
All real numbers
10
12
24. Fill in the property that justifies each step.
14 = 2(x – 3)
14 = 2x – 6
Distributive Property
14 + 6 = 2x – 6 + 6
Add. Property of Equality
20 = 2x + 0
Additive Inverse
20 = 2x
Additive Identity
Given
Multiplication Property of Equality
10 = 1x
Multiplicative Inverse
10 = x
Multiplicative Identity
x = 10
Symmetric Property
25. Fill in the property that justifies each step.
Solution
(3x + 9) + 1 > 13
Property
Given
3x + (9 + 1) > 13
Associative Property of Addition
3x + 10 > 13
Substitution
3x + 10 + (-10) > 13 + (-10)
Addition Property of Inequality
3x + 0 > 3
Additive Inverse
3x > 3
Additive Identity
3x >
Multiplication Property of Inequality
3
1x > 1
Multiplicative Inverse
x>1
Multiplicative Identity
26. There are four mistakes in the proof below. Find and correct the mistakes.
(x + 3)
5 > -10
Given
5(x + 3) > -10
Associative Property of Multiplication
Commutative
5x + 15 > -10
Distributive Property
5x + 15 + (-15) > -10 + (-15)
Addition Property of Equality Inequality
5x + 0 > -25
Inverse Property of Multiplication Addition
5x > -25
Identity Property of Addition
5x > -25 •
Multiplication Property of Inequality
1x > -5
Identity Property of Multiplication Inverse
x>-5
Identity Property of Multiplication