### Simple Inequlatities, Interval Notation, and, Numbers

- Find a rational number between 3 and π.
- Find an irrational number that is between 1.299 and 1.3.
- Solve for all real values of
*x*. Graph your answer on a number line and write your answer in interval notation.
*x* + 3 > 5
- -
*x* > 4
- |
*x*| > 7
- |
*x*| ≤ 5

After attempting above problems,

- discuss solving simple equations and inequalitites
- review conclustions about absolute values in inequalities
- review conclusions about negative coefficients on variables in inequlaities
- discuss numbers more: how to identify an irrational number and why the square root of a prime number is irrational
- review exponents and do a few more of those

4. Solve the following linear equations:

- 5
*x* + 2 = 12
- 3
*x* + 5 = 2*x* + 7
- 3(
*x* + 2) = 2(*x* - 1) + 7

5. Solve the linear inequalities

- 3
*x* + 7 ≤ 8
- 5 - 2
*x* ≥ 13
- 7
*x* + 4 < 2(*x* -3)

6. Solve a few more absolute value problems and write your answer in interval notation where appropriate.

- 5|
*x*| + 2 = 12
- |5
*x* + 2| = 12
- 5|
*x*| + 2 > 12
- 5|
*x*| + 2 ≤ 12

7. Solve and write your answer in interval notation where appropriate.

- |2
*x* - 14| = 4
- |8 - 2
*x*| ≥ 10
- 3|7
*x* + 3| - 2 = 43
- 8|
*x*+2| = -16
- 3|7
*x* + 3| - 2 ≤ 43
- 3|7
*x* + 3| - 2 > 43
- 2|7
*x* + 3| + 8 ≥ 8
- 2|7
*x* + 3| + 8 ≤ 8
- 2|7
*x* + 3| + 8 < 8
- 2|7
*x* + 3| + 8 > 8

coming next:
Inequalities with 'and' and 'or' in general (already did limited cases with inequalities)
Absolute Value as a Distance discussion and problems
Polynomials with a single variable.
Prove equality of two expressions with Properties: Associative, Commutative, and Distributative
Simplifying messy intervals.
More complicated inequalities involving absoltue value
Simple set theory and logic: unions, intersections, not in a set and simplifying interval notation