Solve the following system of equations in R. |x+2|-x x <2 - Vidyadip

Question

Solve the following system of equations in R. $\frac{|\text{x}+2|-\text{x}}{\text{x}}<2$

✓

Answer

We have, $\frac{|\text{x}+2|-\text{x}}{\text{x}}<0$ $\frac{|\text{x}+2|-\text{x}}{\text{x}}-2<0$ $\frac{|\text{x}+2|-\text{x}-2\text{x}}{\text{x}}<0$ $\frac{|\text{x}+2|-3\text{x}}{\text{x}}<0\ ...(\text{i})$ Case 1: When $|\text{x}+2|\geq0$ $\Rightarrow\frac{\text{x}+2-3\text{x}}{\text{x}}<0$ ⇒ - 2x + 2 < 0 ⇒ -2x < - 2 and x > 0 ⇒ x > 1 ...(ii) case2: |x + 2|< 0 x < -2 ⇒ -(x + 2)- 3x < 0 ⇒ - x - 2 - 3x < 0 ⇒ -4x - 2 < 0 ⇒ -4x < 2 $\Rightarrow\text{x}>\frac{-1}{2}\ ...(\text{iii})$ and x < 0 Combining (ii) and (iii), we get $(-\infty,0)\cup(1,\infty)$ as the solution set.

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 "(Each question 3 marks)" from Linear Inequations→Linear Inequations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

Solve the following system of equations in R. $\frac{7\text{x}-1}{2}<-3,\frac{3\text{x}+8}{5}+11<0$

Decide among the following sets which sets are subsets of each another:
A = {X : X $\in$ R} and x satisfies x2 - 8x + 12 = 0}, B = {2, 4, 6} , C = {2, 4, 6, 8, ...}, D = {6}

Find the rational number having the following decimal expansions:$0.\overline{3}$

Find the domain of the following real valued functions of real variable: $\text{f(x)}=\frac{1}{\text{x}-7}$

The Sum of first three terms of a G.P. is $16$ and the Sum of the next three term is $128$. determine the first term, the common ratio and the Sum to n terms of the G.P.

$\text{a}^2\sin(\text{B}-\text{C})=(\text{b}^2-\text{c}^2)\sin\text{A}$

Find the equation of the straight line which makes a triangle of area $96\sqrt{3}$ with the axes and perpendicular from the origin to it makes an angle of 30° with Y-axis.

Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}. Verify the following identities: $\text{A}\cap(\text{B}\cup\text{C})=(\text{A}\cap\text{B})\cup(\text{A}\cap\text{C})$

Find the value of ${({a^2} + \sqrt {{a^2} - 1} )^4} + {({a^2} - \sqrt {{a^2} - 1} )^4}$