Algebraic Expressions and Number Operations

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This content covers algebraic expressions, absolute value, addition, subtraction, and practice examples. It includes evaluating expressions, working with intervals, absolute values, and operations involving positive and negative numbers.

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Review of Section 1 1) Write as an algebraic expression a) Five more than 8 times a number

Evaluate when x = 10 2) 7 + 5x

Write in interval notation and graph 3) {x| -1 < x 4}

Write in set-builder notation and graph 4) [-2, 5)

Chapter 1 Section 2 Operations with Read Numbers and Simplifying Algebraic Expressions

Absolute Value |a| Distance from 0 to a on the number line. Positive value Evaluate 1) | -4 | 2) | 3.5| 3) - | -2 |

Addition (+) + (+) = (+) ( - ) + ( - ) = ( - ) (+) + ( - ) = sign of larger value subtract to get the number

Addition Examples 4 + 2 = 6 - 4 + (-3) = - 7 - 4 + 5 = 1 - 4 + 3 = -1

Try 1) -12 + (-14) 2) 2 + (- 9) 3) - 9 + 3 4) 4 + 6

Subtract Use the definition of subtraction Add the opposite of the second number Meaning, change the subtraction sign to addition and take the opposite of the second number

Subtraction 7 10 Change the sign to addition and take the opposite of 10 so 7 + (- 10) -7 10 Same as above: - 7 + (- 10)

Example - 7 (- 10) Change the subtraction sign to addition and take the opposite of 10 - 7 + 10

Work the following 4a) -12 + (-14) 5) 5 + (-2) 6) 6 13 7) 5.1 (-4.2)

Multiplication, Division ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) + +=+ - -=+ - +=- + -=-

Multiplication, Division Like signs, answer is positive Unlike signs, answer is negative + + -

Give the sign(+, -) of the answer 1) -3 + (-8) 2) -7 + 4 3) 3 15 4) 8 (-10) 5) - 4 5 6) 9(-10) 7) (-3)(-11) 8) (-4)(-2)(5) 9) ? -3 6 -2 12 10) 5 ? ? -102 11)

Answers 1) - 2) - 3) - 4) + 5) - 6) - 7) + 8) 9) 10) 11) -

Evaluate 32 7) 7(-5) 8) (-6)(- 4) 12) ? -4 -3 4 -5 13) 9 ? 9) -2(-3)(-5) ( ) 2 ?-3 10) ? -72 11)

Order of Operations ( ) 2 ?3-52+12 2 -4 ( ) 2- 6-9 ( 14) 3 4+3 -2 15) ) ?

Distributive Property -2(3x + 5) distribute the -2 5(4x 3) distribute the 5 4(7x 3) 10x distribute the 4 and simplify

Answers - 6x 10 20x 15 18x + 12

Distributive Property Simplify 16) 5(4x 3) 17) 4(7x 3) 10x

Similar Terms Similar terms Same variable, same exponent 4x, 3x 4 pears, 3 pears 2 apple pies, 6 apple pies Another example

Combine Similar Terms 4 apples + 3 apples 3 pears + 2 apples + 6 oranges + 2 pears 3 bags in which each bag has 4 bananas and 3 oranges. Can you represent this another way?