Download App

Linear Inequations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLinear Inequations1 Mark
Question
Write the solution set of the inequation $|\text{x}-1|\geq|\text{x}-3|$
✓

Answer

$|\text{x}-1|\geq|\text{x}-3|$
$\Rightarrow|\text{x}-1|-|\text{x}-3|\geq0$
By equating the expression within the modulus to zero, we get x = 1, 3.
These point divide real line in three parts viz. $(-\infty,1),[1,3)$ and $[3\infty).$
Case 1: When $-\infty<\text{x}<1$
|x - 1| = -(x - 1) and |x - 3| = -(x - 3)
$\therefore|\text{x}-1|-|\text{x}-3|\geq0$
$\Rightarrow-2\geq0$ which is not true.
So, the given inequation has no solution for $\text{x}\in(-\infty,1)$
Case 2: When $1\geq\text{x}<3$
|x - 1| = -(x - 1) and |x - 3| = -(x - 3)
$\therefore|\text{x}-1|-|\text{x}-3|\geq0$
⇒ (x - 1) + (x - 3) $\geq$ 0
$\Rightarrow2\text{x}-4\geq0$
$\Rightarrow\text{x}\geq2$
But $1\leq\text{x}\leq3$
Therefore in case the solution set of the given inequation is [2, 3)
Case 3: When $3\leq\text{x}<\infty$
|x - 1| = -(x - 1) and |x - 3| = -(x - 3)
$\therefore|\text{x}-1|-|\text{x}-3|\geq0$
⇒ (x - 1) + (x - 3) $\geq$ 0
$\Rightarrow2\geq0$
The solution set of the given inequation is $[3,\infty)$
Combining 1 and 3 we obtain that the solution set of the given inequation is $[2,3)\cup[3,\infty)=[2,\infty)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the following Question.(1 Marks)" from Linear Inequations→Linear Inequations — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Examine the continuity of :
$f(x)=\frac{x^2-9}{x-3}$, for $x \neq 3$
$=8$ for $x=3$, at $x=3$.
→
Write the conjugates of the following complex numbers: √2 + √3 i
→
If $\text{a}=\text{b}\cos\frac{2\pi}{3}=\text{c}\cos\frac{4\pi}{3},$ then write the value of ab + bc + ca.
→
Write the coordinates of the in-centre of the triangle with vertices at (0, 0), (5, 0) and (0, 12).
→
Express the following numbers in the form x + iy:

$e^{\frac{-4 \pi}{3} i}$

→
Find the nth term and hence find the 8th term of the following HPs.

$\frac{1}{5}, \frac{1}{10}, \frac{1}{15}, \frac{1}{20}, \ldots$

→
Evaluate the following:

$i ^{116}$

→
Write the set of value if n for which the statement p(n): 2n < n! is true.
→
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
→
Let $S_n$ denote the sum of first $n$ terms of an $A.P.$ If $S_{2n} = 3 S_n$, then $S_{3n} : S_n$ is equal to:
→