7.4 Solving Rational Equations & Inequalities

Day 2

Rational Inequalities

Solve for x using the calculator

2 2 1 02

x x xx

2x

2 2 12

x x xx

Set the equation equal to zero

Graph in your calculator

Where is the graph GREATER THAN zero? Use the trace function.

You can also go to the table and look at the values to see when the y-values start to get larger than zero.

Solve for x using the calculator

Rational Inequalities

Set the equation equal to zero

Graph in your calculator

Step 3: Use the zero feature to find where the graph of y1 lies above the x-axis.

Solution:

Step 2: Put the left hand side into y1 and the right hand side into y2.

6 42x

6 4 02x

2,21

xx

Zero: x = 1/2

VA: x = 2

7 25x

7 2 05x

Solve for x using the calculator

Rational Inequalities

Set the equation equal to zero

Graph in your calculator

Step 3: Use the zero feature to find where the graph of y1 lies above the x-axis.

Solution: 5.15 x

Step 2: Put the left hand side into y1 and the right hand side into y2.

Zero: x = -1.5

VA: x = -5

Solve for x using the calculator

Rational Inequalities

Set the equation equal to zero

Graph in your calculator

Step 3: Use the zero feature to find where the graph of y1 lies above the x-axis.

Solution:

Step 2: Put the left hand side into y1 and the right hand side into y2.

2)1()23(

xx

02)1()23(

xx

10 x

Zero: x = 0

VA: x = 1

Solve for x using the calculator

Rational Inequalities

Set the equation equal to zero

Graph in your calculator

Step 3: Use the zero feature to find where the graph of y1 lies above the x-axis.

Solution:

Step 2: Put the left hand side into y1 and the right hand side into y2.

)5(3

)7(4

xx

0)5(

3)7(

4

xx

75 x

VA: x = -5

VA: x = 7

Rational Inequalities Solve for x using the calculator

Step 2: Put the left hand side into y1 and the right hand side into y2.

Step 1: Set up the inequality 8007.79300,50966

2

2

tt

From 1990 to 2001, the number d (in thousands) of doctors in the United States can be modeled by the function where t is the number of

years since 1990. When were there fewer than 800,000 doctors?

7.79300,50966

2

2

tt

Step 3: Use the intersect feature to find where the graph of y1 lies below the graph of y2.

Solution: In the years 1990-1999, there were fewer than 800,000 doctors

Rate – of – Work Problems It takes 7 hours for John to paint a house. Jerry can paint the same house in 5 hours. How long will it take them to paint the house if they work together?

Identify the variable TIME or t = time it takes John and Jerry to paint the house together.

Write an equation. 157

tt

Solve the equation. 1

3512

t

3512 t

92.21235

t

In Class ASSIGNMENT

Homework: Page 600#1 – 17 odds

Worksheet – Homework if you don’t finish it in class