INEQUALITIES

September 20, 2010

ACT Opener

1. Solve 2n – 6 = 10 – 14n.A. 1B. -1C. 0D. -2E. 2

2. Solve (2/3)h – 5 = h + 7F. -36G. 36H. -24J. 24K. 20

3. Solve for x: 5x + 3 = 2x -9

4. Solve for k: 5k + 12 – 2k = 37 + 2k - 11

Inequality Symbols

< less than

> greater than

open dot

≤ less than or equal to

≥ greater than or equal to

closed dot

Inequality Symbols

The Open Dot We only use the “open dot” to graph less than and greater than inequalities.

< or >

The Closed Dot We only use the “closed dot” to graph less than or equal to and greater than or equal to inequalities

< or >

Inequality Shading

If x is greater than (greater than or equal to), then shade to the right.

If x is less than (less than or equal to), the shade to the left.

An Inequality Special Situation If you multiply or divide by a negative

number, reverse the symbol.

Otherwise, we solve inequalities just like equations!

Examples: Assume the domain is all real numbers

x > 3

a < -1

-5 < b

Examples: Assume the domain is all real numbers

4 > x

x = -4

x ≠ 3

Solve and Graph Examples

3x-5 < 2

Solve and Graph Examples

5x + 4 > 19

Solve and Graph Examples

2x – 7 < 3

Examples

4 - 3x > -2

Examples

6x – 3 < 7 + 4x

Examples

2(w-8) + 9 > 3(4 – w) - 4

Examples

8 – 2b > 4 - b

Examples

4(2 – v) > -(v – 5)

Exit Slip

Solving Inequalities with Multiple Operations AND

Solving Inequalities with Variables on Both SidesPage 26 and 27 b

Assignment