Question
Solve the inequality
Solve for a
Solve for h
Solve for n
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a≥s2thn1,h<0,n<0,t>0a≥s2thn1,h<0,n>0,t<0a≥s2thn1,h>0,n<0,t<0a≥s2thn1,h>0,n>0,t>0a≤s2thn1,h<0,n<0,t<0a≤s2thn1,h<0,n>0,t>0a≤s2thn1,h>0,n<0,t>0a≤s2thn1,h>0,n>0,t<0
Evaluate
40≤s×sthan×40
Multiply
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Evaluate
s×sthan×40
Multiply the terms
s2than×40
Use the commutative property to reorder the terms
40s2than
40≤40s2than
Rewrite the expression
40≤40s2thna
Swap the sides of the inequality
40s2thna≥40
Divide both sides
40s2thn40s2thna≥40s2thn40
Divide the numbers
a≥40s2thn40
Divide the numbers
a≥s2thn1
Rewrite the inequalities
{a≥s2thn1thn>0{a≤s2thn1thn<0
Calculate
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Calculate
thn>0
Separate the inequality into 2 possible cases
{t>0hn>0{t<0hn<0
Solve the inequality
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Evaluate
hn>0
Separate the inequality into 2 possible cases
{h>0n>0{h<0n<0
Find the union
{h<0n<0{h>0n>0
⎩⎨⎧t>0{h<0n<0{h>0n>0{t<0hn<0
Solve the inequality
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Evaluate
hn<0
Separate the inequality into 2 possible cases
{h>0n<0{h<0n>0
Find the union
{h<0n>0{h>0n<0
⎩⎨⎧t>0{h<0n<0{h>0n>0⎩⎨⎧t<0{h<0n>0{h>0n<0
Find the intersection
⎩⎨⎧h<0n<0t>0⎩⎨⎧h>0n>0t>0⎩⎨⎧t<0{h<0n>0{h>0n<0
Find the intersection
⎩⎨⎧h<0n<0t>0⎩⎨⎧h>0n>0t>0⎩⎨⎧h<0n>0t<0⎩⎨⎧h>0n<0t<0
Find the union
⎩⎨⎧h<0n<0t>0⎩⎨⎧h<0n>0t<0⎩⎨⎧h>0n<0t<0⎩⎨⎧h>0n>0t>0
⎩⎨⎧a≥s2thn1⎩⎨⎧h<0n<0t>0⎩⎨⎧h<0n>0t<0⎩⎨⎧h>0n<0t<0⎩⎨⎧h>0n>0t>0{a≤s2thn1thn<0
Calculate
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Calculate
thn<0
Separate the inequality into 2 possible cases
{t>0hn<0{t<0hn>0
Solve the inequality
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Evaluate
hn<0
Separate the inequality into 2 possible cases
{h>0n<0{h<0n>0
Find the union
{h<0n>0{h>0n<0
⎩⎨⎧t>0{h<0n>0{h>0n<0{t<0hn>0
Solve the inequality
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Evaluate
hn>0
Separate the inequality into 2 possible cases
{h>0n>0{h<0n<0
Find the union
{h<0n<0{h>0n>0
⎩⎨⎧t>0{h<0n>0{h>0n<0⎩⎨⎧t<0{h<0n<0{h>0n>0
Find the intersection
⎩⎨⎧h<0n>0t>0⎩⎨⎧h>0n<0t>0⎩⎨⎧t<0{h<0n<0{h>0n>0
Find the intersection
⎩⎨⎧h<0n>0t>0⎩⎨⎧h>0n<0t>0⎩⎨⎧h<0n<0t<0⎩⎨⎧h>0n>0t<0
Find the union
⎩⎨⎧h<0n<0t<0⎩⎨⎧h<0n>0t>0⎩⎨⎧h>0n<0t>0⎩⎨⎧h>0n>0t<0
⎩⎨⎧a≥s2thn1⎩⎨⎧h<0n<0t>0⎩⎨⎧h<0n>0t<0⎩⎨⎧h>0n<0t<0⎩⎨⎧h>0n>0t>0⎩⎨⎧a≤s2thn1⎩⎨⎧h<0n<0t<0⎩⎨⎧h<0n>0t>0⎩⎨⎧h>0n<0t>0⎩⎨⎧h>0n>0t<0
Calculate
⎩⎨⎧a≥s2thn1h<0n<0t>0⎩⎨⎧a≥s2thn1h<0n>0t<0⎩⎨⎧a≥s2thn1h>0n<0t<0⎩⎨⎧a≥s2thn1h>0n>0t>0⎩⎨⎧a≤s2thn1⎩⎨⎧h<0n<0t<0⎩⎨⎧h<0n>0t>0⎩⎨⎧h>0n<0t>0⎩⎨⎧h>0n>0t<0
Calculate
⎩⎨⎧a≥s2thn1h<0n<0t>0⎩⎨⎧a≥s2thn1h<0n>0t<0⎩⎨⎧a≥s2thn1h>0n<0t<0⎩⎨⎧a≥s2thn1h>0n>0t>0⎩⎨⎧a≤s2thn1h<0n<0t<0⎩⎨⎧a≤s2thn1h<0n>0t>0⎩⎨⎧a≤s2thn1h>0n<0t>0⎩⎨⎧a≤s2thn1h>0n>0t<0
Solution
a≥s2thn1,h<0,n<0,t>0a≥s2thn1,h<0,n>0,t<0a≥s2thn1,h>0,n<0,t<0a≥s2thn1,h>0,n>0,t>0a≤s2thn1,h<0,n<0,t<0a≤s2thn1,h<0,n>0,t>0a≤s2thn1,h>0,n<0,t>0a≤s2thn1,h>0,n>0,t<0
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