Question

solve 2x-3/4 >= 1/2 ,x belongs to {1,2,....,8}

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Chapter 4 Linear Inequations.
M.L. Aggarwal. Class 10th.​

Answer 1

Step-by-step explanation:

Given:-

(2x-3)/4≥1/2 ,x belongs to 1,2,..,8

To find:-

Solve (2x-3)/4≥1/2 ,x belongs to 1,2,..,8

Solution:-

Given in-equation is (2x-3)/4≥1/2

On multiplying with 4 on both sides

=>(2x-3)×4/4≥(1/2)×4

=>2x-3≥2

On adding 3 on both sides

=>2x-3+3≥2+3

=>2x+0≥5

=>2x≥5

on dividing by 2 on both sides then

=>2x/2≥5/2

=>x≥5/2 or 2.5

The value of x is greater than or equal to 5/2 or 2.5

If x belongs to natural numbers then

x=3,4,...

But given that x belongs to 1,2,...,8

according to the given condition

x=3,4,5,6,7,8

Answer:-

The solution set of x={3,4,5,6,7,8}

Check:-

1)If x=3 then (2x-3)/4

LHS=[2(3)-3]/4

=(6-3)/4

=2/4

=1/2

LHS=RHS

2)If x=4 then(2x-3)/4

LHS=[2(4)-3]/4

=(8-3)/4

=5/4

≥1/2

LHS=RHS

3)If x=5 then (2x-3)/4

LHS=[2(5)-3)]/4

=(10-3)/4

=7/4

≥1/2

LHS=RHS

4)If x=6 then (2x-3)/4

LHS=[2(6)-3]/4

=(12-3)/4

=9/4

≥1/2

LHS=RHS

5)If x=7 then (2x-3)/4

LHS=[2(7)-3]/4

=(14-3)/4

=11/4

≥1/2

LHS=RHS

6)If x=8 then (2x-3)/4

LHS=[2(8)-3]/4

=(16-3)/4

=13/4

≥1/2

LHS =RHS

Given in-equation is true for the solution set x={3,4,5,6,7,8}

Verified

Answer 2

Answer:

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