Download Concepts 1.1

Bell Work
10/17/14
Solve the inequality.
1.
 4 x  5  19
2.
22  3x  7
3.
4  x  5  32
4.
35  7  x  2
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Heading
5/24/2017
3.5 Solving Inequalities with
Variables on Both Sides
TSWBAT: solve an inequality that has
variables on both sides.
Students solve multi-step problems, including word
problems, involving linear equations and linear
inequalities in one variable and provide
justification for each step.
Notes
• Review
1.
3x  9  8 x  6
 3x
 3x
9  5x  6
6
6
15  5x
5
5
3  x
3.
 4x  7  7  4x
 4x
 4x
77
All Real Numbers
2.
6  x  2  2  x  2
6x  12  2x  4
 2x
 2x
4x  12  4
12 12
4 x  16
4
4
x  4
Notes
• Rules for Solving Inequalities.
• Solve just like you would an equation.
• ONLY ONE EXCEPTION.
• If you multiply or
divide by a negative
number you MUST
reverse the inequality
symbol.
Notes
Solve the inequality.
Ex.
6x  7  4x 11
 4x
 4x
2x  7  11
7 7
2x  18
2
2
x9
Now you try.
Ex.
4 x  5  8x  3
 4x
 4x
5  4x  3
3
3
8  4x
4 4
2x
x2
Notes
Solve the inequality. (Compare and Contrast)
Ex.
Ex.
2x  8  4x 10
 2x
 2x
8  6x 10
 10
 10
18  6x
6
6
3 x
x3
2x  8  4x 10
 4x
 4x
6x  8  10
8 8
6x  18
6
6
x 3
Notes
Solve the inequality.
Ex.
4  x  3  2  x  5
4x  12  2x  10
 2x
 2x
2x 12  10
 12  12
2x  22
2
2
x  11
Now you try.
Ex.
2  x  6  6  x  4
2x  12  6x  24
 2x
 2x
12  4x  24
 24
 24
36  4x
4
4
9  x
x  9
Notes
Solve the inequality.
Ex.
5x  6  5x 12
 5x
 5x
6  12
All Real Numbers
Now you try.
Ex.
3x  7  3  x  4 
3x  7  3x  12
 3x
 3x
7  12
No Solution
Notes
Solve the inequality.
Ex.
2x  8x  9  4x 1
6x  4x  8
 4x  4x
2x  8
2
2
x  44
Notes
Solve the inequality.
Ex.
2  x 1  6 x  5  2  x  2  9
2x  2  6 x  5  2x  4  9
4x  3  2x 13
 4x
 4x
3  2x  13
 13
13
10  2x
2
2
5  x
x  5
Summary
Write a summary about today’s lesson.
To solve multi-step inequalities you first
possible If
distribute and/or combine like terms if ________.
sides move one of the
there are variables on both _____
variable
variables to the other side. Now isolate the ________
completely.
Today’s Homework
Rules for Homework
1. Pencil ONLY.
2. Must show all of your work.
• NO WORK = NO CREDIT
3. Must attempt EVERY problem.
4. Always check your answers.
Homework
Solve the inequality.
1.
6x  5  2x  3
3.5
2.
5 x  6  2 x  15
3.
4 x  9  7 x  12
4.
 5 x  4  3 x  6
5.
3  x  7   2  x  3
6.
7  x  2  5  x  4
7.
4  x  4  8  x  2
8.
 2  x  3  4  x  3
9.
7x  5  7x  6
10.
 3  4x  4x  5
3  x  5  4  2  x  6   3
12.
4  x  5  6  7  x  2   9
11.
Ticket Out the Door
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Solve the inequality.
3x  8  7 x  4