Warm-up

1. Determine the x-intercept (s) and y-intercept from the graph below.

Determine what this viewing rectangle illustrates. 2. [-20, 40, 5] by [-10, 30, 2]

3. Solve this equation: 4x + 5 = 29

Homework: pg. 104, (1-45 odds)Problems 10-14 must show checking your answer.

Answers: 1. x-intercepts = (3,0) and (-7,0) y-intercept = (0,21) it’s a reflection

2. The x window’s min is at -20, max at 40 increasing in increments of 5. The y window’s min is at -10, max at 30 increasing in increments of 2. 3. x = 6

Announcements:

Ch 1 Learning Goal: The student will be able to understand functions by solving and graphing all types of equations and inequalities.

Today’s Objective: Be able to solve a rational equations with variables

Lesson 1.2A Linear Equations and Rational Equations

A linear equation in one variable x is an equation that can be written in the form of

ax + b = 0,

where a and b are real numbers

and a 0.

Steps for Solving a Linear Equation:1. Simplify the algebraic expression on each

side by removing grouping symbols and combining like terms.

2. Collect all the variable terms on one side

and all the numbers, or constant terms, on the other side.

3. Isolate the variable and solve.

4. Check the proposed solution in the original equation.

Example 1: Solving a Linear Equation Involving Fractions

2 12

4 3

x x

Given.

2 112 2 12

4 3

x x

Find LCD.

3(x+2)-4(x-1)=24

3x +6-4x+4 = 24

-x = 14

Solve by Distributive Property and combine like terms.

Solve and check.x = -14

You try these:

4(2x +1) = 29 + 3(2x -5)

3 5 5

4 14 7

x x

Answers: x = 5, x=1

Example 2:1 1 3

5 2x x

1 1 310 10

5 2x x

x x

10 = 2x +15

x = -5/2

You Try: 5 17 1

2 18 3x x

Answer: x = 3

Example 3: Solving Rational Equations

Write problem.

Objective – try to clear fractions.

Multiply both sides by

(x-3) to cancel it out on the left side

Distribute the (x-3) on the right side

Cross out the (x-3) to get rid of them in denominators

93

3

3

xx

x

)93

3()3(

3)3(

xx

x

xx

9)3()3

3()3(

3)3( x

xx

x

xx

)3(9)3

3()3(

3)3( x

xx

x

xx

Example Continued

X = 3 + 9(x-3)X = 3 + 9x – 27X = 9x – 24

-8x = -24

X = 3

SimplifyDistribute the 9Subtract 3 and -27Subtract 9x from both sides

Divide by -8.Unfortunately not a solution

because of the excluded values. The solution is an empty set, 0 .

You Try!

Write problem

Multiply both sides by 3(x-2)

Distribute the 3(x-2) to the right side

Cancel out any 3(x-2)

Multiply

3

2

2

2

2

xx

x

)3

2

2

2()2(3

2)2(3

xx

x

xx

)3

2)(2(3)

2

2)(2(3

2)2(3 x

xx

x

xx

)2(3)3

2()

2

2)(2(3

2)2(3 x

xx

x

xx

)42(63 xx

Distribute the negative

Solve for x.

Not a solution because of the excluded values.

The solution is an empty set, 0

4223 xx

2

105

2103

4263

x

x

xx

xx

Summary: What is a rational equation? Give an example of this type of equation.

Homework: WS1.1 pg. 104, (1-45 odd) Problems 10-14 must show checking

your answer.