Algebra 2- Solving Equations and Expressions

Página 1

Questions:

Find the value of each expression. (Note: Use Order of Operations, PEMDAS)

1. 8(3+6) 2. 10-8/2 3. 14(2)-5 4. [9+3(5-7)] /3 5. [6-12-8^2] 6. 17(2+26)/4=119

Answer: 72 Answer: 6 Answer:23 Answer:1 Answer:-2 Do yourself!

Evaluate each expression if x=4, y=2, and z=6

10. z-x+y 11. x+(y-1)^2 12. x+[3(y+z)-y]

Answer:0 Answer:-23 Answer: 18

Evaluate each expression.

13. √9 14. √16 15. √100 16. √169 17. - √4 18. -√25 19. √4/9 20. √36/49

Answer:3 =4 =10 =13 = -2 = -5 =2/3 =6/7

1-2 Properties of Real Numbers

Information:

real numbers :all the numbers that you use in everyday use.

real number= rational and irrational numbers.

What are rational and irrational numbers?

rational numbers: integers like 1,2,3,4,5, etc. They can also be fractions and decimals that repeat and does not go on forever.

irrational numbers: decimals that don't repeat and goes on forever. Example: √110, π

Classifying Numbers

natural (N) whole(W) integers(Z)

rational(Q) real (R) Irrational (I)

Questions:

Name the sets of numbers to which each number belongs.

1. -4 Z, Q, R 2. 45 N, W, Z, Q, R 3. 6.233333333... Q,R

Name the property illustrated by each equation.

7. 2/3 x 3/2=1 8. (a+4)+2= a+ (4+2) 9. 4x+0=4x

Answer: Multiplication Property Answer: Associative Property Answer: Addition Identity

Identify the addition inverse and multiplication inverse for each number.

10. -8 11. 1/3 12. 1.5

Answer:8, -1/8 Answer: -1/3, 3 Answer: -1.5, 2/3

Simplify each expression.

13. 3x+4y-5x 14. 9p-2n+4p+2n 15. 3(5c+4d) + 6(d-2c)

Answer: -2x+4y Answer:13p Answer: 3c+18d

1-3 Solving Equations

Information:

Open Sentence: A mathematical sentence containing one or more variables.

Equation: a mathematical sentence stating that two mathematical expressions are equal.

Write an algebraic expression to represent each verbal expression. BOLD=Answer

4. five increased by four times a number. 5+4n

5. twice a number decreased by the cube of the same number. 2n-n^3

Write a verbal expression to represent each statement. BOLD=Answer

6. 9n-3= 6 9 times a number decreased by 3 is 6

7. 5+3x^2=2x 5 plus 3 times the square of a number is twice that number.

Name the property illustrated by each statement. BOLD=Answer

8. (3x+2) -5= (3x+2)-5 9. IF 4c =15, then 4c+2= 15+2

Reflexive Property Addition Property (=)

Solve each equation. Check your solution.

10. y+14=-7 11. 7+3x=49 12. -4 (b+7) = -12 13. 7q+q-3q= -24 14. 1.8a-5= -2.3

y=-21 x=14 b= -4 q= -4.8 a=1.5

1-4 Solving Absolute Value

Questions:

absolute value: a number is distance from 0 on a number line. Since distance is positive the absolute value is positive.

Information:

empty set: For example |x|= -5 is not a true statement which means it has no solution. The solution set for this type of equation.

Questions:

Evaluate each expression if a= -4 and b= 1.5

5. |a+12| 8 6. |-6b| 9 7. - |a+21| -17

Solve each equation. Check your solutions.

8. |x+4|=17 9. |b+15|=3

x=13 x= -12, -18

[ -21,13]

Evaluate each equation if a= 5, b=6, and c= 2.8.

17.|-3a| 15 18. |4b| 24 19. |a+5| 0 20. |2-b| 4 22. |4a+7| 13

28. |a-b| -- |10c-a| DO YOURSELF

1-5 Solving Inequalities

Information:

Trichotomy Property: property of order

Addition Inequalities

In Words: For any real numbers, a,b,c, if a>b, then a+c>b+c

Addition Inequality

Words: For any real numbers a,b,c. If a>b, then a+c>b+c. If a

Example: 3

Subtraction Inequality

Words: For any real numbers a,b,c. If a>b, then a-c> b+c. If a

Example:2>7 ; 2-8>7-8

Multiplication Inequality

Words: For any real numbers a,b,c. C is positive if a then ac>bc. If ben acb then ac>bc

-2

Division Inequality

Words: For any real numbers a,b,c. C is positive if abc. If bve if ab, then ac>bc.

Example: -2

set-builder notation: The solution set of an inequality. For example {x|x>9}

Interval notation: the solution set of an inequality being described x≥ -2 (+,-2)

Questions:

Solve each inequality. Describe the solution set using set builder notation or interval notation.

1-3, 1-4

1-5, 1-6