Download Name: : :___ Algebra 2A Review of Chapter 6 Study Guide Topics

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Algebra 2A
Review of Chapter 6
Study Guide
Topics for the Quest:
 Solving Multi-Step Equations
Know your Steps for Solving a Multi-Step Equation!
Recall: No Solution (untrue statement) and All Real Numbers (True statement)
Examples:
Solve.
1.
2
m  1  11
3
3. 2  5t  3  5t  7
2. 23a  1  7a  3a  2  12
4.
1
4h  6  9h  6  7h  3
2
 Properties and Algebraic Proof
LIST OF PROPERTIES
(A)
(B)
(C)
(D)
(E)
(F)
Additive Identity
Multiplicative Identity
Subtraction Property of Equality
Division Property of Equality
Distributive Property
Associative Property
(G)
(H)
(I)
(J)
(K)
(L)
Symmetric Property of Equality
Addition Property of Equality
Multiplication Property of Equality
Substitution Property
Commutative Property
Multiplicative Property of Zero
Examples:
Name the property illustrated by each statement.
5. If 6  4  10 then 10  6  4 _______
6. If x  2  7 then x  5 _______
7. 3  2  11  3  2  11 _______
8. 1  8  8
9. If
x
 7 then x  14 _______
2
11. 10  0
_______
_______
10. 0  3  3 _______
12. 8  12  12  8 _______
13. 25  4  72  4  2572 _______
14. If 2x  14 then x  7 _______
15. 257  4  2528 _______
16. 5a  3  5  a  5  3 _______
Name the Property used in each step.
17. 5  2 x  4  17  6 x _________________________________
5  2x  4  17  6x _________________________________
9  2x  17  6x _________________________________
9  4x  17 _________________________________
4x  8 _________________________________
x  2 _________________________________
Solve the equation and name the property used in each step.
18. 2  3x  1  4x  15
 Solving Inequalities and graphing results
Recall: When dividing or multiplying by a negative number, be sure to switch the inequality sign!
Recall: No Solution (untrue statement) so no graph and All Real Numbers (True statement) so shade entire line.
Solve each inequality, then graph the solutions on a number line.
19. 4  2x  6  3x  7  2x  8
20.  5x  3  5x  1
Solve each inequality, then graph the solutions on a number line.
21. 7a  3  7a  1
22. 24x  3  18
 Solving Combined Inequalities (“and”/“or” statements) and graphing results
Recall: “And” statements are intersections (overlapping) of graphs
“Or” statements are unions (everything on same number line) of graphs
Recall: No Solution (untrue statement) so no graph and All Real Numbers (True statement) so shade entire line.
1
x5
2
23.  7  4x  11  9
24.  4x  3  11 or
25. 2x  3  11 or 3x  2  8  2x
26. 13  3x  2 and 53x  2  18x  11
27. 2  5x  12 and
3
x28
4
28.  3  x or 
x
 2
3
 Solving Absolute Value Equalities and Inequalities and graphing results
Recall: Isolate the absolute value part of the equality/inequality first!
Rewrite abs. value equality as an “OR” statement
Rewrite abs. value inequality as combined inequality: Great”OR” Less”AND”
“And” statements are intersections (overlapping) of graphs
“Or” statements are unions (everything on same number line) of graphs
1
x 1  6
4
29. 2 3  2 x  1  11
30. 3 
31. 2 x  3  5  7
32. 8x  4  2  10