EQUATIONSEQUATIONSTIU College Entrance Test

ReviewMath Session 6

REVIEW OF EQUATIONS

What type of equation is this?

1. 3 5 1 2x x 22. 8 16 0x x

23. 4 1 2x 2

4. 6 103x

x

linear

quadratic

quadratic

linear

What type of equation is this?3 5

1. 2 4 4xx

2. 2 6x

3. 3 2 8x 2 3 6

4. A B C

rational

radical

absolute value

literal

RATIONAL Equations

4 3 9

3 3x x x x

4 3 93 3

3 3x x x x

x x x x

4 3 3 9x x

4 3 3 3 9 3

3 3

x x x x x x

x x x x

Multiply both sides by the LCD

(Cont’d) 4 3 3 9x x

4 3 9 9x x

7 9 9x

7 0x 7 07 7x

0x

We have to check if 0 is a possible solution. Look at The original problem.

What is the DOMAIN of the equation?

x cannot be 0 or -3. Why?

4 3 93 3x x x x

any number is undefined.

0 Why?

12Definition of division: 6 because 2 6 12.

2

5So,if , what should be so that 0 =5?

0n n n

n cannot be any number defined in math.any number

is undefined.0

RADICAL Equations

How do you check if you are correct?Substitute 38 into the original equation.

2 6x

222 6x

2 36 38x

x

ABSOLUTE VALUE Equations

What is x?

5x

The replacement set for x is {-5, 5}.

How about for 3 2 8?x

3 2 8 x

3 2 8x

Two values for x:

How do you check if you are correct?Substitute 10/3 and -2 one at a time into

the original equation.

First solution:

Second solution:

3 1010

3

x

x

3 6 2

xx

3 2 8 x

LITERAL Equations

Solve for B:

Get rid of the denominators by multiplying both sides of the equation by the LCD.

2 3 6A B C

2 3 6ABC ABC

A B C

2 3 6BC AC AB

2 3 6BC AC AB Keep in mind which variable

you want to isolate.Put the terms with B on the

same side of the equation.

c c

2 6 3BC AB AC 2 6 3B C A AC

3

2 6AC

BC A