Chapter+3

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 * Chapter 3 - Solving Linear Equations**

** Lesson 3.1 ** **Solve One-Step Equations**

 * Key Vocabulary**:
 * ** Inverse operations **- two operations that undo each other, such as addition and subtraction.
 * ** Equivalent equations **- when you perform the same inverse operation on each side of an equation. Also known as equations that have the same solution(s). pg. 84

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 * Extra Help:**

** Lesson 3.2 ** ** Solve Two-Step Equations **

 * Key Vocabulary: **
 * like terms
 * input
 * output

The equation x/2+5 = 11 involves two operations performed on //x:// division by 2 and addition by 5. You typically solve such an equation by applying the inverse operations in the reverse order of the order of operations. This is shown on the table below:


 * ** Operations performed on //x// ** || **Operations to isolate //x//** ||
 * # Divide by 2.
 * 1) Add 5 || # Subtract 5.
 * 2) Multiply by 2. ||

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 * Extra Help:**


 * Practice Problems:**

a) 3x+7=19 b) 7d-1=13 c) 10=7-m

** Lesson 3.3 ** **Solve Multi-Step Equations**
**Key Vocabulary** distributive property reciprocal

Solving a linear equation may take more that two steps. Start by simplifying one or both sides of the equation, if possible. Then use inverse operations to isolate the variable.

**Solve 8x-3x-10=20**
 * Example:**

8x-3x-10=20 Write original equation 5x-10=20 Combine like terms. 5x-10+10=20+10 Add 10 to each side 5x=30 Simplify __5x__ =__30__ Divide 5 by each side 5 5 x=6 Simplify

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 * Extra Help**


 * Practice Problems:**

a) p+2p-3=6 b) 11w-9-7w=15 c) 35=-5+2x-7x

** Lesson 3.4 ** **Solve Equations with Variables on Both Sides**
identity [pg. 973]
 * Key Vocabulary:**

Some equations have variables on both sides. To solve such equations, you can collect the variable terms on one side of the equation and the constant terms on the other side of the equation.

Example: Solve 7-8x=4x-17

7-8x=4x-17 Write original equation 7-8x+8x=4x-17+8x Add 8x to each side 7=12x-17 Simplify 24=12x Add 17 to each side 2=x Simplify

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 * Extra Help**


 * Practice Problems:**

a) 12y+6=6(2y+1) b) 12+5v=2v-9 c) w+3=w+6

** Lesson 3.5 ** **Write Ratios and Proportions**
A **ratio** uses division to compare 2 quantities. You can write the ratio of 2 quantities a and b, where b is not equal to 0. in 3 ways.

a to b a:b __a__ b

Each ratio is read "the ratio of a to b." Ratios should be written in simplest form.

Example:


 * VOLLEYBALL** A volleyball team plays 14 home matches and 10 aways matches.

a. Find the ratio of the home matches to the away matches. b. Find the ratio of the home matches to all matches.

Solution

a. __home matches__ = __14__ = __7__ 7:5 7 to 5 away matches 10 5 b. __home matches__ = __14__ = __7__ 7:12 7 to 12 all matches 24 12

A proportion is and equation that states 2 ratios are equivalent.

Example: Solve

__11__ = __x__ 6 30

30⋅__11__ = 30⋅__x__ 6 30

** Lesson 3.7 ** **Solve Percent Problems**
For this lesson, all you need to know is the formula below:

__a__ = __p__ b 100

p= percent a= part of base b= base

Example: What is the % of 25 is 17

First write the formula __a__ = __p__ b 100

Substitute the numbers __17__ = __p__ 25 100

Cross multiply 1700=25p

Divide each side by 25 68=p

17 is 68% of 25 ( I like to think of it as 17=.68⋅25