Równania z wartością bezwzględną - Matematyka Liceum i Technikum

In this video, I show you how to solve absolute value equations, including equations where the absolute value involves linear expressions, fractions, radicals, and cases where one absolute value is nested within another. I demonstrate the technique for two variants—positive and negative—for each equation, as well as how to handle situations where the equation contradicts or the absolute value is zero. I discuss the algebraic manipulations necessary to simplify equations, including removing parentheses, dividing sides, multiplying by irrational numbers, reducing terms, and solving linear equations in one and two steps. I also show how to solve absolute value equations on both sides using the identity |A| = |B| ⇔ A = B ∨ A = –B, and how to treat equations containing absolute values ​​in the numerators of fractions. In cases where absolute values ​​are nested, I present an approach to writing the inner value as a separate equation. I show when we solve only one variant and how to recognize and write a contradiction. Table of Contents: 1. Reviewing the definition of absolute value 2. Solving the equation |x| = 4 3. Solving the equation 3 · |x| = 15 4. Solving the equation |2x – 1| = 5 5. Contradictory equations with an absolute value less than zero 6. Equations where the absolute value equals zero 7. Equation with a fraction and a square root in the absolute value 8. Nested equation: | |x – 3| | = 2 9. Nested equation: | |3x + 1| – 6 | = 2 10. Equation with absolute value on both sides 11. Equation with fractions and radicals on both sides 12. Equation with algebraic expressions and absolute value on both sides You can find more in the playlist:    • ALGEBRA RÓWNANIA NIERÓWNOŚCI UKŁADY RÓWNAŃ   and:    • Rozwiązywanie równań - 192 rozwiązane zadania   You can get EASY ACCESS to all my math lessons using my website: www.matmagwiazdy.pl On this channel, you will find full lectures - 100% of the lessons - in Mathematics for Primary School, High School, and Technical School. Good luck :) Tomasz D. Gwiazda **CHAPTERS** 0:00 Absolute Value Equations |x|=4 3|x|=15 4:05 Problems: |2x−1|=5 |2x−1|=−5 |2x−1|+8=5 7:10 Problems: |2x−1|=0 |2x−1|+5=5 9:54 Problems: |(x−2)/√5|=√3/3 14:19 Problems: ||x−3||=2 17:10 Problems: ||3x+1|−6|=2 21:34 Problems: |x−5|=|2x+1| 24:20 Tasks: |(x−1)/(2√2)|=|3x/√5| 28:43 Tasks: 2+|x−1|=5−|2x+3| **END**