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Solve the following linear in-equations and graph the solution set on a real number line.(iii) 2\left( 3x-5 \right)>5\left( 13-2x \right),x\in W(iv) 3x-9\le 4x-7<2x+5,x\in R
Class 10 | Frank | ICSE | Linear Inequations | Maths
Solve the following linear in-equations and graph the solution set on a real number line.(iii) 2\left( 3x-5 \right)>5\left( 13-2x \right),x\in W(iv) 3x-9\le 4x-7<2x+5,x\in R

From the question it is given that,

2(3x-5)>(13-2x)
6x-10>65-10x

So, by transposing we get,

6x+10x>65+10

16x>75

x>75/16

x>4\frac{11}{16}

As per the condition given in the question, x\in W.

Therefore, solution set x>4\frac{11}{16}

Set can be represented in number line as,

Solution: –

From the question,

Consider 3x-9\le 4x-7

So, by transposing we get,

4x-3x\ge -9+7

x\ge -2

Now, consider 4x-7\le 2x+5

By transposing we get,

4x-2x<5+7

2x<12

x<12/2

x<6

As per the condition given in the question, x\in R.

Therefore, solution set =[-2\le x<6]

Set can be represented in number line as,

i

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