Question

Question 5 Solve the given inequality for real x: 4x + 3 < 5x + 7

Class X1 - Maths -Linear Inequalities Page 122

Answer 1

4x + 3 < 5x + 7
subtract 4 both sides,
4x + 3 - 3 < 5x + 7 - 3
=> 4x < 5x + 4
subtract ' 5x ' both sides ,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality]

4x - 5x < 5x + 4 - 5
-x < 4
now, multiple with (-1) then, sign of inequality change .
-x.(-1) > 4(-1)
x > -4

hence, x€ ( -4 , ∞)

Answer 2

Given : Inequality  4x+3<5x+7     , x ∈ R  

To Find : Solve

Solution:

4x+3 < 5x + 7

Subtract 4x from both sides

=> 4x + 3  - 4x < 5x  + 7  - 4x

=> 3  <  x  + 7

Subtract 7 from both sides

=> 3 - 7 < x + 7 - 7

=> - 4 < x

=> x  > - 4

x ∈ ( - 4 , ∞ )

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