Solve the given inequality for real x:3(2x−1)≥4(3x−2)−5(2−x)

3(2x−1)≥4(3x−2)−5(2−x)⇒3(2x−1)≥205(3x−2)−4(2−x)⇒3(2x−1)≥2015x−10−8+4x⇒3(2x−1)≥2019x−18⇒20(2x−1)≥3(19x−18)⇒40x−20≥57x−54⇒−20+54≥57x−40⇒34≥17x⇒2≥xThus, 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]

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Solve the given inequality for real x:{(2x-1)}{3} {(3x-2)}{4}

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Solve the given inequality for real $x : \frac{( 2 x - 1 )}{3} \geq \frac{( 3 x - 2 )}{4} - \frac{( 2 - x )}{5}$

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Solve the given inequality for real

x : \frac{( 2 x - 1 )}{3} \geq \frac{( 3 x - 2 )}{4} - \frac{( 2 - x )}{5}

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Text solutionVerified

\frac{( 2 x - 1 )}{3} \geq \frac{( 3 x - 2 )}{4} - \frac{( 2 - x )}{5}

\Rightarrow \frac{( 2 x - 1 )}{3} \geq \frac{5 ( 3 x - 2 ) - 4 ( 2 - x )}{20}

\Rightarrow \frac{( 2 x - 1 )}{3} \geq \frac{15 x - 10 - 8 + 4 x}{20}

\Rightarrow \frac{( 2 x - 1 )}{3} \geq \frac{19 x - 18}{20}

\Rightarrow 20 (2 x - 1) \geq 3 (19 x - 18)

\Rightarrow 40 x - 20 \geq 57 x - 54

\Rightarrow - 20 + 54 \geq 57 x - 40

\Rightarrow 34 \geq 17 x

\Rightarrow 2 \geq 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

(- \infty, 2]

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Question Text	Solve the given inequality for real $x : \frac{( 2 x - 1 )}{3} \geq \frac{( 3 x - 2 )}{4} - \frac{( 2 - x )}{5}$
Answer Type	Text solution:1
Upvotes	150

Solve the given inequality for real x:3(2x−1)​≥4(3x−2)​−5(2−x)​

Text solutionVerified

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Solve the given inequality for real $x : \frac{( 2 x - 1 )}{3} \geq \frac{( 3 x - 2 )}{4} - \frac{( 2 - x )}{5}$