Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
1.
13- 3x ≥ x +5
3. ­2(x­3) = 3(2x­1)
2. 3y - 6 +4y < 12 -5y - 6
3. 3y - 2 < 1- 5y
4.
5
2
1
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
1.
13- 3x ≥ x +5
2
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
2. 3y - 6 +4y < 12 -5y - 6
3
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
3. ­2(x­3) = 3(2x­1)
4
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
3.
3y - 2 < 1- 5y
5
2
5
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
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Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
Let's Have A Look ....
Place a > or < sign that makes the statement true.
5
­7
Now lets multiply each side by (­1) What do you notice???
7
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
Let's Have A Look ....
Place a > or < sign that makes the statement true.
­6
­18
Now lets divide each side by (­6) What do you notice???
8
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
1) When you multiply or divide a inequality by a positive number the inequality remains the same.
Example)
5 > ­1
5(3) > (­1)(3)
15 > ­3
2) When you multiply or divide a inequality by a "negative number" the inequality must be reversed(switched) in order to remain true.
12 > ­10
12 ÷(­2) ­10÷(­2)
Switch inequality since divided by a negative
12 ÷(­2) < ­10÷(­2)
FIX
­6 < 5
NOTE:
When solving an inequality, we use the same strategy as for solving an equation. BUT Remember when we divide or multiply by a negative number, we reverse the inequality sign.
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Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
Switch the inequality sign ONLY when you divide or multiple by a negative 10
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
Solve each inequality. Graph the solution.
1) x ­2
≤
5
3) ­6r ≥ 72
2) k ≥ 10
­7
4) 13t ≤ ­26
11
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
What if you solve for a negative "variable" 1) ­2n ­ 5 > 6n + 7 1) ­2n ­ 5 > 6n + 7 12
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
The grade 12 Culinary Class decided to raise money by organizing a supper for the seniors home. The cost of preparing the food is $675 and the students are charging $9.00 a plate. How many seniors must buy suppers in order to make a profit more than $765.
13
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
Page 305 ­ 306
Don't need to graph or verify * Questions7,8,9,10,11,12
*
Test on _____________ 14
Day 14_6.5 Solving Inequalities Using mult and Division_2017.notebook February 27, 2017
1) ­1.6n ­5 > 4.1n +10.96 Step 1) Bring all letters to one side and number to the other.
­1.6n ­5 +5 > 4.1n +10.96 +5
Add 5 to each side
­1.6n > 4.1n +15.96 ­1.6n ­ 4.1n > 4.1n ­ 4.1n +15.96 ­5.7n > 15.96 ­5.7n 15.96 >
­5.7 ­5.7
Subtract 4.1n from each side.
Step 2)Divide each side by the number in front of the letter. Divide each side by "­5.7" and since negative reverse the sign.
n < ­2.8
The solution is all numbers smaller than ­2.8
Check you work
Choose a number less than ­2.8.........­3
Substitute n = ­3 into the original inequality
See if left hand side is greater than right hand side
­1.6n ­5 > 4.1n +10.96 Left hand side
Right hand side
4.1n +10.96
­1.6n ­5 ­1.6(­3) ­5 4.1 (­3)+10.96
4.8 ­ 5
­12.3 +10.96
0.2
­1.34
0.2 > ­1.34
IT WORKS
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