Mathematics
Represent the following inequalities on real number lines :
(i) 2x - 1 < 5
(ii) 3x + 1 ≥ -5
(iii) 2(2x - 3) ≤ 6
(iv) -4 < x < 4
(v) -2 ≤ x < 5
(vi) 8 ≥ x > -3
(vii) -5 < x ≤ -1
Linear Inequations
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Answer
(i) 2x - 1 < 5
⇒ 2x < 5 + 1
⇒ 2x < 6
⇒ x < 3
Solution on the number line is :
(ii) 3x + 1 ≥ -5
⇒ 3x ≥ -5 - 1
⇒ 3x ≥ -6
Dividing both sides by 3 we get,
⇒ x ≥ -2
Solution on the number line is :
(iii) 2(2x - 3) ≤ 6
⇒ 4x - 6 ≤ 6
⇒ 4x ≤ 6 + 6
⇒ 4x ≤ 12
Dividing both sides by 4 we get,
⇒ x ≤ 3
Solution on the number line is :
(iv) -4 < x < 4
Solution on the number line is :
(v) -2 ≤ x < 5
Solution on the number line is :
(vi) 8 ≥ x > -3
Solution on the number line is :
(vii) -5 < x ≤ -1
Solution on the number line is :
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