Transcript 3.3

MULTIPLICATION
&
DIVISION
12𝑏 ≥ 60
12𝑏 ≥ 60
12𝑏 60
≥
12
12
12𝑏 ≥ 60
12𝑏 60
≥
12
12
𝑏≥5
12𝑏 ≥ 60
12𝑏 60
≥
12
12
𝑏≥5
16𝑑 ≤ 64
12𝑏 ≥ 60
16𝑑 ≤ 64
12𝑏 60
≥
12
12
16𝑑 64
≤
16
16
𝑏≥5
12𝑏 ≥ 60
16𝑑 ≤ 64
12𝑏 60
≥
12
12
16𝑑 64
≤
16
16
𝑏≥5
𝑑≤4
12𝑏 ≥ 60
16𝑑 ≤ 64
12𝑏 60
≥
12
12
16𝑑 64
≤
16
16
𝑏≥5
𝑑≤4
9𝑛 > 36
12𝑏 ≥ 60
16𝑑 ≤ 64
9𝑛 > 36
12𝑏 60
≥
12
12
16𝑑 64
≤
16
16
9𝑛 36
>
9
9
𝑏≥5
𝑑≤4
12𝑏 ≥ 60
16𝑑 ≤ 64
9𝑛 > 36
12𝑏 60
≥
12
12
16𝑑 64
≤
16
16
9𝑛 36
>
9
9
𝑏≥5
𝑑≤4
𝑛>4
𝑛
≥8
8
𝑛
≥8
8
8
1
𝑛
8
≥
8
1
8
1
𝑛
≥8
8
8
1
𝑛
8
≥
8
1
𝑛 ≥ 64
8
1
𝑛
≥8
8
8
1
𝑦
< 14
7
𝑛
8
≥
8
1
𝑛 ≥ 64
8
1
𝑛
≥8
8
8
1
𝑦
< 14
7
𝑛
8
≥
8
1
𝑛 ≥ 64
8
1
7
1
𝑦
14
<
7
1
7
1
𝑛
≥8
8
8
1
𝑦
< 14
7
𝑛
8
≥
8
1
𝑛 ≥ 64
8
1
7
1
𝑦
14
<
7
1
𝑦 < 98
7
1
15 5
≤ 𝑥
8
2
15 5
≤ 𝑥
8
2
2
5
15
5
≤
8
2
𝑥
1
2
5
15 5
≤ 𝑥
8
2
2
5
15
5
≤
8
2
3
≤𝑥
4
𝑥
1
2
5
15 5
≤ 𝑥
8
2
2
5
15
5
≤
8
2
3
≤𝑥
4
2.6𝑣 ≥ 6.5
𝑥
1
2
5
15 5
≤ 𝑥
8
2
2
5
15
5
≤
8
2
3
≤𝑥
4
2.6𝑣 ≥ 6.5
𝑥
1
2
5
1
2.6
2.6𝑣
6.5
≥
1
1
1
2.6
15 5
≤ 𝑥
8
2
2
5
15
5
≤
8
2
3
≤𝑥
4
2.6𝑣 ≥ 6.5
𝑥
1
2
5
1
2.6
2.6𝑣
6.5
≥
1
1
𝑣 ≥ 2.5
1
2.6
−5 ≤
𝑦
9
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
9
1
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
9
1
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−2𝑥
10
>
−2
−2
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−2𝑥
10
>
−2
−2
𝑥 > −5
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−2𝑥
10
>
−2
−2
𝑥 > −5
What went wrong?
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−2𝑥
10
>
−2
−2
𝑥 > −5
What went wrong?
When multiplying or
dividing by a NEGATIVE
value, you must switch the
direction of the inequality.
−5 ≤
9
1
𝑦
9
−5
𝑦
≤
1
9
−45 ≤ 𝑦
−2𝑥 > 10
9
1
−2𝑥
10
>
−2
−2
𝑥 > −5
What went wrong?
When multiplying or
dividing by a NEGATIVE
value, you must switch the
direction of the inequality.
𝑥 < −5
4𝑟
>8
5
4𝑟
>8
5
−
5
𝑘
>−
7
14
4𝑟
>8
5
−
5
𝑘
>−
7
14
−92 < 23𝑦
4𝑟
>8
5
−
5
𝑘
>−
7
14
−92 < 23𝑦
−6𝑘 ≤ 54
3.3: 2 – 30 (evens)