Question

3x +2 <0 and 4x -320

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Answer #1

Answer: 2 3 3 4 OR xin {Phi }OR 'NO SOLUTION'

Explanation: The given inequalities are,

3x+2<0 and x-3>0  

Let us take first inequality

3x+2<0

subtract 2 from both sides

3x+2-2<0-2

3x<-2

divide both sides by 3

rac{3x}{3}<rac{-2}{3}

2-3

So,

3 -------------------------------------------------- (1)

Now, takes the second inequality,

x-3>0

add 3 in both sides

4x-3+3ge0+3

4xge3

Now, divide both sides by 4

rac{4x}{4}ge rac{3}{4}

2

So,

xin [rac{3}{4}, +infty) ------------------------------------------------- (2)

Since the inequality is 'and' type so, the solution will be the intersection of these two solutions. So,

2 3 3 4

Since, there is no common between the two solution sets. So, the solution of inequality will be

xin {Phi }

OR x has no solution which satisfy both the inequalities at the same time.

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