Mathematics
Solve the inequation given below. Write the solution set and represent it on the number line:
-2 + 10x ≤ 13x + 10 < 24 + 10x, x ∈ Z
Linear Inequations
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Answer
Given,
⇒ -2 + 10x ≤ 13x + 10 < 24 + 10x
Solving L.H.S. of the inequation,
⇒ -2 + 10x ≤ 13x + 10
⇒ 13x + 10 ≥ -2 + 10x
⇒ 13x - 10x ≥ -2 - 10
⇒ 3x ≥ -12
⇒ x ≥
⇒ x ≥ -4 …….(1)
Solving R.H.S. of the inequation,
⇒ 13x + 10 < 24 + 10x
⇒ 13x - 10x < 24 - 10
⇒ 3x < 14
⇒ x <
⇒ x < 4.6 …………(2)
From (1) and (2) we get,
⇒ -4 ≤ x < 4.6
Since, x ∈ Z
Hence, solution set = {-4, -3, -2, -1, 0, 1, 2, 3, 4}.
Solution on the number line is :
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