Solve the given inequality for real x: x+frac | vedclass

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

Question

(A) Given inequality: $x+\frac{x}{2}+\frac{x}{3} < 11$
Taking $x$ as a common factor:
$x(1+\frac{1}{2}+\frac{1}{3}) < 11$
Finding the common

Vedclass · Accepted Answer

$(-\infty, 6)$

Vedclass · Answer

(A) Given inequality: $x+\frac{x}{2}+\frac{x}{3} < 11$
Taking $x$ as a common factor:
$x(1+\frac{1}{2}+\frac{1}{3}) < 11$
Finding the common denominator for the terms inside the bracket:
$x(\frac{6+3+2}{6}) < 11$
$x(\frac{11}{6}) < 11$
Multiply both sides by $\frac{6}{11}$:
$x < 11 	imes \frac{6}{11}$
$x < 6$
Thus,all real numbers $x$ which are less than $6$ are the solutions of the given inequality.
Hence,the solution set is $(-\infty, 6)$.

Solve the given inequality for real $x$: $x+\frac{x}{2}+\frac{x}{3} < 11$

Similar Questions

Solve the given inequality and show the graph of the solution on a number line:
$5x - 3 \geq 3x - 5$

The set $A = \{x : |2x + 3| < 7\}$ is equal to which of the following sets?

If $|x+2| \leq 9,$ then which of the following is true?

Solve the following inequality: $|4-x|+1 < 3$

Solve $-5 \leq \frac{5-3x}{2} \leq 8$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module