Download Lesson 2.8 Day 2 Solving More Complicated

Lesson 2.8 Day 3 Solving More
Complicated Linear Inequalities
Student Handout
DATE_______
Foundations of College Algebra
Chapter 2
Linear Inequalities
Solving More Complicated
Inequalities
Lesson 2.8 Objective Day 2
I will increase my knowledge of linear
inequalities by solving more complicated
problems that require using both addition and
multiplication, problems with fractions, and
problems
Solve, graph and write answer in interval
notation.
1.Write orig problem:
5x – (x – 2) < 7x – 5
2. Distribute
3. combine
4. move variable left;
5. move constant right;
6. undo coefficient
Graph:
Write solution in interval notation:
1
Solving more complicated inequalities
1.
2.
if needed.
down original inequality
to remove grouping symbols
3.
like terms on each side of equal
sign separately
4. Move all variables left
5.
all constants right
6.
coefficient of variable by multiplying
or dividing.
Remember to
inequality SIGN
if multiplying or dividing by a
2
NUMBER
Solve, graph and write answer in interval
notation.
1. Write problem:
3x + 2 – 5 > – x + 7 + 2x
2. Distribution
not needed
3. combine
4. move variable left;
5. move constant right;
6. undo coefficient
Graph:
Write solution in interval notation:
3
4
Solve, graph and write answer in interval
notation.
1.Write prob.:
5(x – 3) – 7x ≥ 4(x – 3) + 9
2. Distribute
3. combine
4. move variable left;
5. move constant right;
6. undo coefficient
Graph:
Write solution in interval notation:
5
Solve, graph and write answer in interval
notation.
1.Write:
– 2 (x – 3) – 1 < 1 (5 – r)
3
2
2
2a. Clear denomin:
2. Distribute
3. combine
4. move variable left;
5. move constant right;
6. undo coefficient
Graph:
Write solution in interval notation:
6
1
Lesson 2.8 Day 3 Solving More
Complicated Linear Inequalities
Student Handout
DATE_______
Solve, graph and write answer in interval
notation.
1.Write:
1 (x + 3) + 2 ≤ 3 (x + 8)
4
4
2a. Clear denomin:
2. Distribute
3. combine
4. move variable left;
5. move constant right;
6. undo coefficient
Graph:
Write solution in interval notation:
Solve, graph and write in interval notation
2 ≤ 3x – 1 ≤ 8
1. Check in correct form:
2. Add:
3. Divide:
4. Graph
Write in interval notation
7
NESTED or THREE PART INEQUALITIES FORM
2<x≤7
- the variable will be
two number
10
Solve, graph and write in interval notation
–4 ≤ 2x–1≤8
3
1. Check in correct form:
2. Clear denominator:
- the
on the
number is always placed
side
3. Add:
- the
on the
number is always placed
side
5. Graph:
- BOTH symbols are always going in
direction and are either < or ≤
-
the variable in the center
8
following all the rules you already know.
Solve, graph and write in interval notation
4 ≤ 3x – 5 < 6
1. Check in correct form:
4. Divide:
Write in interval notation
11
Homework
Page 175
Page 175 Day 1: 41, 42, 44, 47, 48, 50, 52, 53,
56, 58, 59, 62, 64, 65, 68, 70, 71, 72
2. Add 5 to ALL 3 PARTS:
3. Divide ALL 3 PARTS by 3:
4. Graph
Write in interval notation
9
12
2