Solve the given inequality for real x: frac{( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given inequality: $\frac{(2x-1)}{3} \geq \frac{(3x-2)}{4} - \frac{(2-x)}{5}$ Taking the $LCM$ of the denominators on the $RHS$: $\frac{(2x-1)}{3}

Vedclass · Accepted Answer

$(-\infty, 2]$

Vedclass · Answer

(A) Given inequality: $\frac{(2x-1)}{3} \geq \frac{(3x-2)}{4} - \frac{(2-x)}{5}$ Taking the $LCM$ of the denominators on the $RHS$: $\frac{(2x-1)}{3} \geq \frac{5(3x-2) - 4(2-x)}{20}$ Expanding the terms: $\frac{(2x-1)}{3} \geq \frac{15x - 10 - 8 + 4x}{20}$ Simplifying: $\frac{(2x-1)}{3} \geq \frac{19x - 18}{20}$ Cross-multiplying: $20(2x - 1) \geq 3(19x - 18)$ $40x - 20 \geq 57x - 54$ Rearranging terms: $-20 + 54 \geq 57x - 40x$ $34 \geq 17x$ Dividing by $17$: $2 \geq x$ or $x \leq 2$ Thus,the solution set is $(-\infty, 2]$.

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

Similar Questions

If $|x-2| \geq |x-4|$ then $x \in \ldots$

If $\frac{1}{x-4} < 0$,where $x \in R$,then $x \in$

Solve the following inequality and represent it on a number line: $\frac{2x-1}{3} + 5 < \frac{3x-1}{2} - 2$

If $x + y + z = a$,then what is the value of $x + y + z$?

Solve the system of inequalities:
$3x - 7 < 5 + x$ ..... $(1)$
$11 - 5x \leqslant 1$ ..... $(2)$
and represent the solutions on the number line.

Vedclass Test Series

Exam Paper Generator

Online Exam Module