Question:
Solve for x, the inequalities in |x – 1| ≤ 5, |x| ≥ 2
Solution:
|x – 1|≤ 5
There are two cases,
1:-
x – 1 ≤ 5
Adding 1 to LHS and RHS
⇒ x ≤ 6
2:-
⇒ -(x – 1) ≤ 5
⇒ -x + 1 ≤ 5
Subtracting 1 from LHS and RHS,
⇒ -x ≤ 4
⇒ x ≥ -4
From cases 1 and 2, we have
⇒ -4 ≤ x ≤ 6 …[i]
Also,
|x| ≥ 2
⇒ x ≥ 2 and
⇒ -x ≥ 2
⇒ x ≤ -2
⇒ x ∈ (∞, -2] ∪ [2, ∞) …[ii]
Combining equation [i] and [ii], we get
x ∈ [-4, -2] ∪ [2, 6]
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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