Question

Represent the solutions of: – 1 < x
2
+ 1 ≤ 3, x ε I (set of integers) on number line.


With the solution

Answer 1

Answer:

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Class 12

>>Applied Mathematics

>>Quantification and Numerical Applications

>>Introduction to Linear Inequalities

>>Solve 3x/5 (2x 1)/3 > 1, x R and represe

Question

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Solve 3x/5 (2x 1)/3 > 1, x R and represent the solution set on the number line.

Medium

Solution

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Given inequation, 3x/5–(2x–1)/3>1

(9x–10x+5)/15>1 [Taking L.C.M]

−x+5>15

−x>15–5

−x>10

x<−10

As x∈R

Hence, the solution set is x:x∈R,x<−10

Representing the solution on a number line:

Answer 2

Answer:

Given: −

3

x

≤

2

x

−1

3

1

<

6

1

Taking L.C.M. of 3,2 and 6 is 6.

−

3

x

×6≤

2

x

×6−

3

4

×6<

6

1

×6

−2x≤3x−8<1

⇒−2x≤3x−8 and 3x−8<1

⇒8≤3x+2x ⇒3x<1+8

⇒8≤5x ⇒3x<9

⇒

5

8

≤x ⇒x<3

∴ The solution set is {x:1.6≤x≤3,xϵ