Unit 6 – Linear Equations and Inequalities
6.1 Solving Equations by Using Inverse Operations
Read page 266 and do the investigate
Addition and Subtraction are inverse operations.
Multiplication and Division are inverse operations.
When solving equations, the goal is to isolate the variable. To do
this, work backwards through the order of operations.
Keep the equation balanced – whatever you do to one side, you
must do to the other side!
Examples:
1. For each statement, write and then solve the equation. Verify
the solution.
a) A number divided by 7 is 2.5.
b) Four times a number plus 6 is -18.
2. Use an arrow diagram to solve each equation.
a) 2x = -18
b) 6x – 8 = 4
3. Solve the question and verify the solution:
5x
 3  12
2
6.1 Assignment (Day 1) Pages 271 – 274: #1 – 13 all
6.1 Continued . . . More examples of solving equations
1.
2.
3(x – 2) = 24
1
2
y  1
6
3
3. Sarah works in a clothing store. She earns $1350 a month plus a
commission of 8% of her sales. One month she earned $1652.
a) Choose a variable to represent Sarah’s sales in dollars. Write an
equation to determine her sales that month.
b) Solve the equation and verify the solution.
4. A rectangle has width 5.4 cm and perimeter 33.4 cm.
a) Write an equation that can be used to determine the length.
b) Solve the equation and verify the solution.
6.1 Assignment (Day 2)
Pages 271 – 274: #11, 12, 14, 17, 18 (a, c, e), 20, 21, 24
AFQ #19, Reflect in journal
6.2 Solving Equations by Using Balance Strategies
Try solving this equation using balancing scales or algebra
tiles: 3a + 9 = 5a + 3
Investigate: p. 275
6.2 Solving Equations by Using Balance Strategies
Solve the following equation using the balancing scales
strategy: 6x + 2 = 10 + 4x
Solve the following equation using the algebra tile
method: -3a + 7 = 2c – 8
Model the solutions symbolically as well.
Watch videos on DVD for solutions.
More examples:
Recall: To solve an equation, we need to isolate the
variable on one side of the equation.
1.
8
  16; y  0
y
2.
2
1
(6 x  9)  (10 x  2)
3
2
3.
1 11
7
x  x
4
4
16
4. A cell phone company offers two plans.
Plan A: 100 free minutes, $0.50 per additional minute
Plan B: 40 free minutes, $0.40 per additional minute
Which time for calls will result in the same cost for both
plans?
a) Model the problem with an equation.
b) Solve the problem and verify the solution.
6.2 Assignment Pages 280 – 283:
#1 – 5
# 6, 8, 10, 11, 17, 19, 21 (every second letter)
#12, 15
AFQ #18 & Reflect in Journal
Mid-Unit Review, Page 286: # 1 – 8 all
6.3 Introduction to Linear Inequalities
Focus: to write and graph inequalities
Investigate: p. 288
We use an inequality sign to represent a range of numbers
rather than a single number.
Inequality signs:
> greater than
< less than
 greater than or equal
 less than or equal
Examples:
1. Define a variable and write an inequality to describe the
following situation: You must have 10 items or less to use
the express checkout line at the grocery store.
2. Is each number a solution of the inequality c  7 ?
Justify your answers.
a) 0
b) -9
c) -7
d) -6.5
3. Graph each inequality on a number line and write four
numbers that are solutions of the inequality.
a)
v > -4
b)
g ≤ 1.5
c)

15
y
7
6.3 Assignment: Pages 292 – 293, #1 – 13
AFQ #11 Reflect in Journal
6.4 Solving Linear Inequalities by Using Addition and
Subtraction
Investigate: page 294
To solve an inequality, we use the same strategy as for
solving an equation: isolate the variable.
Please note that an equation has only one solution and an
inequality has many solutions.
For example:
Equation: x – 6 = -11
Inequality: x – 6 > -11
Examples:
1. Solve and graph each inequality.
a) 8  a  15
b) 5 x 12  4 x  9
2. Ms. Hayes needs to rent 50 chairs for a party. Company
A charges $50 plus $5 per day. Company B charges $70
plus $4 per day. For how many days must Ms. Hayes keep
the chairs for Company A to be less expensive that
Company B?
6.4 Assignment: Pages 297 – 299: #1 – 7 all,
#8, 9 (every second letter), #10 – 12
AFQ #14, Reflect in Journal
6.5 Solving Linear Inequalities by Using Multiplication
and Division
Investigate p. 300
When solving an inequality, if you multiply or divide by
a negative number, you must reverse the inequality
sign!
Examples: Solve, check and graph the solution.
1. 8 x  32
2. 7  3d  6
3.
y
52
3
4. 2 
3
1
w  3w 
4
2
6.5 Assignment
Pages 304 – 306: #1, 3, 5, 6, 8, 10, 13
#7, 9, 11, 12 (every second letter)
AFQ #14, Reflect in Journal
Unit Review
Pages 308 – 309: # 1 - 16 all
See Study Guide on p. 307
For more review, complete the practice test on page
310.
Cumulative Reviews – to prepare for final exam:
Units 1 – 3: p. 148 - 149, #1 - 23
Units 1 – 6: p. 312 – 313, #1 – 15 (Unit 4: #4 - 8)
Units 1 – 9: p. 464 – 467, #1 – 12, #18 – 23
Period 1 Math 90 Final:
Thursday, January 21st, 9 – 11am
Room 332
Bring: textbook, pencils, eraser, calculator, something to
do quietly after the final
I will provide you with a formula sheet.
Final Exam Format:
35 multiple choice (1 mark each) = 35 marks
20 short answer = 43 marks
6 problems = 22 marks