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section 6

100

simplifying expressions

to write an equivalent expression which contains no similar terms

200

n+4-20+7n

11n-20

300

2(x-4)-(x+12)

1x-20

400

simplest form

 lowest terms

500

-n-5(-6-7n)

34n+30

section 7

100

2 step equations

algebraic equation that takes you two steps to solve

200

How do you solve 2 step equations?

1. 1) First, add or subtract both sides of the linear equation by the same number.
2. 2) Secondly, multiply or divide both sides of the linear equation by the same number.
3. 3)* Instead of step #2, always multiply both sides of the equation by the reciprocal of the coefficient of the variable.

300

2x + 3 = 7

x=2

400

3y + 5 = 1

y = -1.333333333

500

x - 3 = 5

x = 8

section 8

100

proportion 

a mathematical comparison between two numbers.

200

Three ways to solve proportions

Vertical

Horizontal

Diagonal (often called "cross-products")

300

how are they written 

Proportions are written like ratios are, for example, a/b = c/d or a:b = c:d.

400

Types of Proportions

Direct Proportion

Inverse Proportion.

500

3:5

09:15

section 9

100

How do you find the absolute value?

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines.

200

absolute value

the magnitude of a real number without regard to its sign.

300

What is the absolute value of -| 4?

the absolute value of -4 is written as |-4|.

400

What is the value of |- 6 |?

the absolute value of −6 will be the distance from −6 to 0 on the number line, and it is 6

500

What is the absolute value of |- 3?

given -3. This number is 3 units away from 0, and thus the absolute value of -3 is 3.

section 10

100

What is a multivariable equation?

A multivariable function is just a function whose input and/or output is made up of multiple numbers. In contrast, a function with single-number inputs and a single-number outputs is called a single-variable function.

200

How do you write a multivariable equation?

The basic rule for solving multi-variable, multi-step equations is to first be sure you have the same number of equations as the number of different variables in the equations. Then, solve one of the equations for one of the variables and plug that expression in for what it equals into the other equation.

300

How do you solve a multivariable system of equations?

Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method. Substitute the solution back into one of the original equations and solve for the third variable.

400

What are some examples of multi-step equations?

• 3y+10.5=6.5+2.5y10(3y+10.5)=10(6.5+2.5y) 3 y + 10.5 = 6.5 + 2.5 y 10 ( 3 y + 10.5 ) = 10 ( 6.5 + 2.5 y )
• 10(3y)+10(10.5)=10(6.5)+10(2.5y) 10 ( 3 y ) + 10 ( 10.5 ) = 10 ( 6.5 ) + 10 ( 2.5 y )
• 30y+105=65+25y 30 y + 105 = 65 + 25 y.

500

8x-3y=-3

x=-3