Algebra Tutorials! Saturday 17th of March

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 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
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 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

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 Ineq. #9:

 Solve for:

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# Variables and Expressions

After completing this lesson, you will be able to:

• Evaluate expressions using the order of operations

In mathematics, we use the order of operations to perform mathematical operations. Always follow this order when performing operations:

1. Simplify within grouping symbols first. Grouping symbols include braces, \{ \} , brackets,[ ] ,and parentheses ( )
2. Evaluate all exponents
3. Perform all multiplication and division, left to right
4. Perform all addition and subtraction, left to right

A good way to remember this is by the saying

Please Excuse My Dear Aunt Salley

The first letter of each word stands for:

P - Parentheses

E - Exponents

M - Multiplication

D - Division

S - Subtraction

Example 1

Evaluate

 = 3 Â· 12 Ã· 4 + 9 Since we have an exponent we do that first 36 Ã· 4 + 9 Since we have multiplication we do that next ( 3 Â· 12 = 36 ) 9 + 9 Since we have division we do that next ( 36 Ã· 4 = 9 ) 18 Last, we do the addition to achieve the final answer of 18

Example 2

Evaluate 8 + 12 Ã· 3

 8 + 12 Ã· 3 = 8 + 4 (Divide 12 by 3) 12 (Add 8 and 4)

Example 3

Evaluate

 = Complete the addition within the parentheses first (2 + 3) 5(25) - 25 Evaluate the exponent 125 - 25 Complete the multiplication ( 5 Â· 25 ) 100 Complete the subtraction

Example 4

 Since we are given values for a and b, we substitute first Complete the addition inside the parentheses Complete the multiplication 2 times 3 and 3 times 1 Add 6 and 3 Multiply (This easily done by multiplying 2 times 9and then dividing by 3)

Example 5

Evaluate for x = 6

 Substitute 6 for each x in the expression 2 times 6 in the numerator and 6 minus 2 in the denominator 12 plus 4 4 16 divided by 4