Statistics

Statistics

Solving a Linear Equation

3 − 6 = 0

Given equation

3 − 6 + 6 = 0 + 6 3 = 6

Add 6 to both sides Combine like terms (-6+6) on left side and (0+6) on right side

3

6 3

Divide both sides by 3

=

3

= 2

After solving an equation, you should check each solution in the original equation. In the above example, check that 2 is a solution by substituting 2 for in the original equation.

Evaluating Expressions

Evaluate 2 + 3 if

= 3 .

2(3) + 3 6 + 3 9

Replace the value of with 3 then evaluate the expression according to the order of operations.

1.3 Exponents

Repeated multiplications can be written in exponential form.

Repeated Multiplication

Exponential Form

2 3

2 × 2 × 2

5 4

(5)(5)(5)(5)

(−4) 3

(−4)(−4)(−4)

(2 ) 4

(2 )(2 )(2 )(2 )

Properties of Exponents

Let and be real numbers, variables, or algebraic expressions, and let and be integers. (Assume all denominators and bases are nonzero.)

Property

Example

5 2 × 5 4 = 5 2+4 = 5 6 = 15626

Add exponents when multiplying.

5 4 ÷ 5 2 = 5 4−2 = 5 2 = 25

Subtract exponents when dividing.

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