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Please help me solve these questions about The Quadratic,Polynomial and Rational Inequalities..

1.) 5x + 6 <_ x + 10 ..(<_ is less than or equal to)
2.) 2>_ -4 - 3x >_ -9
3.)y(11-3y)<10

4.)3/2+t < 2/3-t

Thank you in advance :)

Sagot :

Jers15idn
To graph the inequalities, first graph the following, by placing a broken line if there is only < or >. If not broken line or simply straight line, only if its ≥ or ≤. Then after you graph the equation, to graph the equation just make it the same as like equal sign but broken, or straight..., shade the areas which affect the value of x, lets say if x≤1, then graph the negative parts of x, don't graph the other part which is greater than that.



1.5x+6≤x+10
=4x≤4
=x≤1
set notation:{x/x is a real number, x≤1}
interval notation:(-infinity,1]

2.2≥-4-3x≥-9
=0≥-3x≥-5
=0≤x≤5/3
set notation:{x/x is a real number,0<x<5/3}
interval notation:(0,5/3)

3.y(11-3y)<10
=11y-3y²-10<0
=3y²-11y+10<0
=(3y-5)(y-2)<0
=y<5/3, y<2
set notation:{y/y is a real number, y<5/3 and y<2}
interval notation:(5/3, 2)

4.3/2+t<2/3-t
=2t<13/6
=t<13/12
set notation:{t/t is a real number, t<13/12}
interval notation:(-infinity,13/12)

Hope this helps =)
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