Question

Solve the inequality for real x: 1/5<2x-1< 3/4,x∈R

Answer 1

Answer

3

(2x−1)

≥

4

(3x−2)

−

5

(2−x)

⇒

3

(2x−1)

≥

20

5(3x−2)−4(2−x)

⇒

3

(2x−1)

≥

20

15x−10−8+4x

⇒

3

(2x−1)

≥

20

19x−18

⇒20(2x−1)≥3(19x−18)

⇒40x−20≥57x−54

⇒−20+54≥57x−40

⇒34≥17x

⇒2≥x

Thus, all real numbers x, which are less than or equal to 2, are the solution, of of the given inequality.

Hence, the solution set of the given inequality is (−∞,2]

Answer 2

Question :-

Solve the inequality, for x∈R

$\bf \:\dfrac{1}{5} < 2x - 1 < \dfrac{3}{4}$

Solution :-

$\bf \:\dfrac{1}{5} < 2x - 1 < \dfrac{3}{4}$

Adding 1 in each term, we get

$\bf\implies \:\dfrac{1}{5} + 1 < 2x - 1 + 1< \dfrac{3}{4} + 1$

$\bf\implies \:\dfrac{6}{5} < 2x < \dfrac{7}{4}$

Divide by 2 each term, we get

$\bf\implies \:\dfrac{3}{5} < x < \dfrac{7}{8}$

$\bf\implies \:x∈ (\dfrac{3}{5} , \dfrac{7}{8} )$

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