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in Linear Equations by (15.7k points)

Solve each of the following in equations and represent the solution set on the number line. –2x > 5, where 

(i) x ϵ Z, 

(ii) x ϵ R.

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1 Answer

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by (15.2k points)

(i) -2x > 5, x є Z 

Multiply both the sides by -1 in above equation, 

-2x(-1) > 5(-1) 

2x < -5 

Dividing both the sides by 2 in above equation,

\(\frac{2x}{2} < \frac{-5}{2}\)

x < \(\frac{-5}{2}\)

x < 2.5

Since, x is an integer 

Therefore, possible values of x can be

X = {....., -2, -1,0,1,2}

(ii) -2x > 5, x є R 

Multiply both the sides by -1 in above equation, 

-2x(-1) > 5(-1) 

2x < -5 

Dividing both the sides by 2 in above equation,

\(\frac{2x}{2} < \frac{-5}{2}\)

x < \(\frac{-5}{2}\)

Therefore,

x ∈(-∞, \(\frac{-5}{2}\)\(\big)\)

 x ∈(-∞, \(\frac{-5}{2}\)\(\big)\)

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