Chapter 7 Lesson 5 Solving Inequalities by Multiplying or Dividing pgs. 350 - 354 What you’ll learn: Solve inequalities by multiplying or dividing by.
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Chapter 7 Lesson 5Solving Inequalities by Multiplying or Dividing
pgs. 350 - 354What you’ll learn:
Solve inequalities by multiplying or dividing by positive & negative
numbers
Key Concept: Multiplication & Division
Properties (pg. 350)» Words: When you multiply or divide
each side of an inequality by the same POSITIVE number, the
inequality remains true.
» Symbols: For all numbers a, b, and c, where c > 0
1. If a > b, then ac>bc and a > b c c
2. If a < b, then ac<bc and a < b c c
Key Concept Continued:
» Examples:
2 < 6 3 > -94(2) < 4(6) 3 > -9
8 < 24 3 31 > -3
These properties are also true for a b and a b
Example 1: Multiply or Divide by a Positive Number
» Solve 7y > 63 Check your solution
Write the inequality: 7y > 63 Divide each side by 7: 7y > 63
7 7Simplify: y > 9
The solution is y > 9. You can check this solution by substituting a number greater than 9 into the inequaltiy.
Check: Let’s check with 11 7(11) > 63
77 > 63
Example 1: Another Look
» Solve 6 x Check your solution 7
Write the inequality: 6 x 7
Multiply each side by 7: (7)6 x(7) 7
Simplify: 42 x which also means x 42
The solution is x 42 You can check this solution by substituting 42 or a number less than 42 into the inequality.
Check using 35: 6 35 6 5 7
Example 2: Write an inequality
Julia delivers pizza on weekends. Her average tip is $1.50 for each pizza that she delivers. How many pizzas must she deliver to earn at least $20 in tips?
A. 10 B. 13 C. 14 D. 20Solve: Let x represent the number of pizzas.
1.50 = average per pizza = times x = number of pizzas = at least 20 = total amount to earn
1.50x 20
This works out to 13.333,So at least 14 pizzas.
What happens when each side of an inequality is multiplied or divided by
a negative number? -6 < 11Multiply each side by -1: -1(-6) < -1(11) This inequality is false: 6 < -11
10 5Divide each side by -5: 10 5
-5 -5This inequality is false: -2 -1
The inequalities 6 < -11 and -2 > -1 are both false. However,They would both be true if the inequality symbols were reversed.Change < to > and change > to <. 6 > -11 TRUE -2 < -1 TRUE
Key Concept: Multiplication & Division
Properties (352)Words: When you multiply or divide each of an inequality by the
same negative number, the inequality symbol must be REVERSED for the inequality to remain true.
Symbols: For all numbers a, b, c, where c 0,1. If a > b, then ac < bc and a < b
c c
2. If a < b, then ac> bc and a > b c c
Key Concept Continued:
» Examples:
7 > 1 -4 < 16-2(7) < -2(1) Reverse the symbols-4 16 -14 < -2 -4 -4
1 > -4
This is also true when using and
Example 3: Divide by a Negative Number
» Solve each inequality and check your solution. Then graph the solution on a number line.
15 -5bDivide each side by -5 and reverse the symbol: 15 -5b -5 -5Check this result: -3 b or b -3You can check this result by replacing x in the
original equation with -3 or a number less than -3
Check using -4:15 -5(-4)15 20
See the board for the graph.
Example 3: Multiply by a Negative Number
» Solve the inequality, check your solution and graph the solution on a number line.
6 > x
-7Multiply each side by -7 and reverse the
symbol: -7(6) < x (-7) -7
Check this result: -42 x or x > -42
Check by putting a number greater than -42 in the original inequality. Check using -35:
6 > -35 = 6 > 5 -7
See graph on board.
Your Turn!!Solve, check and graph each
inequality
A. s -3.5 3
B. 15 > 3t
C. 13a -26
D. 7 h -14
(-3) s -3.5(-3) 3 s 10.5
15 3t 3 3 5 > t or t 5
13a -26 13 13 a -2
(-14)7 h (-14) -14
-98 h or h -98
» Extra Practice Is By The Door On Your Way Out!
» Don’t Let The Negative Signs Trip You Up!!
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