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Solve the Following Inequation and Represent the Solution Set on the Number Line 4x - 19 < (3x)/5 - 2 <= (-2)/5 + X, X ∈ R - ICSE Class 10 - Mathematics

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Question

Solve the following inequation and represent the solution set on the number line

`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x`, x ∈ R

Solution

Consider the given inequation

`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R`

`=> 4x - 19 + 2 < (3x)/5 - 2 + 2 <= (-2)/5 + x + 2, x ∈ R`

`=> 4x  - 17 < (3x)/5 <= x + 8/5, x ∈ R`

`=> 4x-(3x)/5<17  "and"  (-8)/5 <=x-(3x)/5,x ∈R `

`=> (20x  - 3x)/5 < 17 and (-8)/5 <= (5x - 3x)/5, x ∈ R`

`=> (17x)/5  <  17`  and `(-8)/5  <= (2x)/5, x ∈ R`

`=> x/5   < 1 and -4 <= x, x ∈ R`

`=> x < 5 and -4 <= x, x ∈ R`

=> -4 ≤ x < 5; where x ∊ R

 The solution set can be represented on a number line as follows:

  Is there an error in this question or solution?

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Solution Solve the Following Inequation and Represent the Solution Set on the Number Line 4x - 19 < (3x)/5 - 2 <= (-2)/5 + X, X ∈ R Concept: Representation of Solution on the Number Line.
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