## Book: RD Sharma - Mathematics

### Chapter: 15. Linear Inequations

#### Subject: Maths - Class 11th

##### Q. No. 8 of Exercise 15.3

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8
##### Solve each of the following system of equations in R.

Subtracting 6 from both the sides, we get–

|x–1|+|x–2|+|x–3|–6≥0

Here, we have 4 cases:

Case 1: –∞ <x<1

For this case, |x–1|=–(x–1), |x–2|=–(x–2) and |x–3|=–(x–3)

–(x–1+x–2+x–3+6)≥0

x–1+x–2+x–3+6<0

3x<0

x<0

xϵ (–∞ , 0) …(1)

Case 2:1<x<2

For this case, |x–1|=x–1, |x–2|=–(x–2) and |x–3|=–(x–3)

x–1–x+2–x+3–6≥0

–x–2≥0

x+2<0

x<–2

Which doesn’t signify the interval

Case 3:2<x<3

For this case, |x–1|=x–1, |x–2|=x–2 and x–3=–(x–3)

x–1+x–2–x+3–6≥0

x–6≥0

x≥ 6

Which doesn’t signify the interval

Case 4:3<x<∞

For this case, |x–1|=x–1, |x–2|=x–2 and |x–3|=x–3

x–1+x–2+x–3–6≥0

x–1+x–2+x–3–6≥0

3x–12>0

x>4

xϵ (4 , ∞ ) …(2)

x ϵ (–∞ , 0) (4 , ∞ ) (from 1 and 2)

We can verify the answers using graph as well.

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