Chapter 3 – Solving Linear Equations

Chapter 3 – Solving Linear Equations Algebra 1 Fall 2013

What will we do in Chapter 3? • Solve linear equations using addition and subtraction • Use linear equations to solve real-life problems • Use multiplication and division to solve linear equations • Solve multi-step equations with variables on both sides of the equals sign • Problem solve with various equations • Learn how to use manipulate decimals in linear equations

3.1 – Solving Equations Using Addition and Subtraction

Objectives • Solve linear equations using addition and subtraction • Use linear equations to solve a variety of real-life problems

What is an Equation? • Has an equal sign • Combination of numbers and variables • Complete thought with numbers and variables on left and right of the equal sign

Equation = Scale • Equations have two sides • Want to keep both sides equal

x = 2 “What value does x have?”

x + 3 = 5 We need x to have a value that will balance the scale!

What if Mental Math isn’t an Option? • We need a process to solve more difficult problems • We need to use inverse operations

Inverse Operations • Definition: • Examples: • Why do we use inverse operations? Operations that undo each other Addition and subtraction Multiplication and division To isolate the variable (get the variable by itself)

State the Inverse Operation • Add 7 • Subtract 3 • Add -11 • Subtract -2

Steps to Solving One-Step Equations • Simplify both sides of the equation • Isolate the variable (by using the inverse operation) • Find the solution • Check your solution

x - 5 = 16 Check

x - 5 = -13 Check

-8 = x – (-4) Check

x - 5 + 2 = -10 Check

Linear Equation • Definition: Equation in which the variable is raised to the first power and does not occur in a denominator inside a square root symbol, or inside absolute value symbols

Find the Linear Equations x + 5 = 9 x2 – 8 = 16 -4 + x = 7 – 3x 16 + 5 = (x/5) (2/x) + 1 = -10 | -17 + x | = 1 x3 + (-3) = 12 -6 = x

Writing Equations • You have x dollars and your friend pays you $6 that he owed you. You now have $14. How much money did you have before your friend paid you?

Writing Equations • A telephone pole extends 4 feet below the ground and 16 feet above the ground. What is the total length x of the telephone pole?

Equivalent Equations • Definition: Two equations that have the same solution 2 + x = 9 x + (-2) = 5 The equations are equivalent because the solution to both equations is x = 7.

Find the Equivalent Equations Draw an arrow from the equations on the left to their equivalent equations on the right. x + 1 = 9 x = -7 8 + x = 5 x + (-3) = -10 4 + (-7) = x 5 + x = 13

Tricky Equations | -6 | + x = 11 | 5 | + 7 = x x + 2 = 11 + 2 x – (-2) = 5 -x = -10

Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 135 #’s 33-44 • P. 137 #’s 66-68

3.2 – Solving Equations Using Multiplication and Division

3.2 – Solving Equations Using Multiplication and Division • Objective: Solve one-step equations using multiplication and division.

State the inverse operation. This problem means -4 times x.

State the inverse operation. This problem means x divided by 5.

Solve the equation.

Solve the equation. This problem means (-2/3) times m equals 10.

REMEMBER! • Dividing by a fraction is the same as multiplying by the reciprocal.

Solve the equation.

Word Problems • You ate three of the eight slices of pizza and you paid $3.30 as your share of the cost. How much did the whole pizza cost? Write an equation!

Word Problems • Each household receives about 676 pieces of junk mail per year. About how many pieces of junk mail does a household receive per week? Write an equation!

Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 142 #’s 28-36, 49-50

3.3 Solving Multi-Step Equations When solving equations you must balance both side. • Simplify both sides of the equation. • Do the opposite operation to both sides. • Addition/Subraction • Multiplication/Division • Check!

Example 1 Solving a Linear Equations ü Solve the equations.

Example 2 Combining Like Terms First ü Solve the equations.

Example 3 Using the Distributive Property ü Solve the equations.

Example 4 Multiplying by a Reciprocal First ü Solve the equations.

Example 5 Real World: Solving Equations A body temperature of 95°F or lower may indicate the medical condition called hypothermia. What temperature in the Celsius scale may indicate hypothermia? Use the formula:

Reminders • 3.1-3.3 Quiz on Thursday, Sept. 12th • Homework: • P. 148-149 #’s 16-36 EVEN’S ONLY

Solving Equations with Variables on Both Sides 3.4 Objectives: • Solve equations with variables on both sides. • Solve equations with variables in the real world. Vocabulary: none

Chapter 3 – Solving Linear Equations