Podcast
Questions and Answers
What are the solutions for the equation $3|x - 7| + 4 = 10$?
What are the solutions for the equation $3|x - 7| + 4 = 10$?
x = 5, x = 9
What is the solution for the equation $-2|x + 4| = 12$?
What is the solution for the equation $-2|x + 4| = 12$?
no solution
What are the solutions for the equation $5 + |2x - 1| = 8$?
What are the solutions for the equation $5 + |2x - 1| = 8$?
x = -1, x = 2
What are the solutions for the equation $x^2 + x - 6 = 0$?
What are the solutions for the equation $x^2 + x - 6 = 0$?
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What are the solutions for the equation $3x^2 - 8 = 10x$?
What are the solutions for the equation $3x^2 - 8 = 10x$?
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What is the solution for the equation $x^2 = -2x - 1$?
What is the solution for the equation $x^2 = -2x - 1$?
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What are the solutions for the equation $3x(x + 1) - x^2 = -4x - 3$?
What are the solutions for the equation $3x(x + 1) - x^2 = -4x - 3$?
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What is the solution for the equation $\sqrt{5x + 2} - 3 = 1$?
What is the solution for the equation $\sqrt{5x + 2} - 3 = 1$?
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What is the solution for the equation $2\sqrt{4x - 1} + 7 = 13$?
What is the solution for the equation $2\sqrt{4x - 1} + 7 = 13$?
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What is the solution for the equation $³\sqrt{x - 5} - 2 = 0$?
What is the solution for the equation $³\sqrt{x - 5} - 2 = 0$?
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What is the solution for the equation $5 + 3⁴\sqrt{2x} = 11$?
What is the solution for the equation $5 + 3⁴\sqrt{2x} = 11$?
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What is the solution for the equation $(x + 5)/(x - 2) = 7/3$?
What is the solution for the equation $(x + 5)/(x - 2) = 7/3$?
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What are the solutions for the equation $(x + 4)/3 = 2/(x - 1)$?
What are the solutions for the equation $(x + 4)/3 = 2/(x - 1)$?
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What is the solution for the equation $-3/x² + 2/x = 1/3$?
What is the solution for the equation $-3/x² + 2/x = 1/3$?
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What is the solution for the equation $2x/(x^2 + 5x + 4) + 3/(x + 1) = 6/(x + 4)$?
What is the solution for the equation $2x/(x^2 + 5x + 4) + 3/(x + 1) = 6/(x + 4)$?
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What are the solutions for the equation $2x^3 - 2x^2 - 40x = 0$?
What are the solutions for the equation $2x^3 - 2x^2 - 40x = 0$?
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What are the solutions for the equation $x^4 + 5x^2 - 36 = 0$?
What are the solutions for the equation $x^4 + 5x^2 - 36 = 0$?
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What are the solutions for the equation $x^3 - 8x^2 + 16x = 0$?
What are the solutions for the equation $x^3 - 8x^2 + 16x = 0$?
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What are the solutions for the equation $x^2/8 + 1 = 3$?
What are the solutions for the equation $x^2/8 + 1 = 3$?
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What is the solution for the equation $|3x - 12| + 16 = 16$?
What is the solution for the equation $|3x - 12| + 16 = 16$?
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Study Notes
Solving Equations Overview
- Various equations produce specific solutions for the variable x, showcasing different mathematical concepts and operations.
Absolute Value Equations
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Equation: 3|x - 7| + 4 = 10
-
Solutions:* x = 5, x = 9
Indicates how absolute values affect the potential solutions by isolating x. -
Equation: -2|x + 4| = 12
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Solution:* No solution
Demonstrates that negative coefficients with absolute values can invalidate solutions. -
Equation: 5 + |2x - 1| = 8
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Solutions:* x = -1, x = 2
Shows how solving absolute value equations includes finding both positive and negative cases.
Quadratic Equations
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Equation: x² + x - 6 = 0
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Solutions:* x = -3, x = 2
Quadratic equations can have two real solutions, determined by factorization. -
Equation: 3x² - 8 = 10x
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Solutions:* x = -2/3, x = 4
Involves rearranging the equation before applying the quadratic formula or factoring. -
Equation: x² = -2x - 1
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Solution:* x = -1
Simplifying to standard form reveals a straightforward solution. -
Equation: x⁴ + 5x² - 36 = 0
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Solutions:* x = ±3i, x = ±2
Illustrates how higher degree polynomials can result in imaginary and real solutions.
Higher-Degree Polynomial Equations
- Equation: 2x³ - 2x² - 40x = 0
-
Solutions:* x = -4, x = 0, x = 5
Factoring out common terms leads to straightforward solutions for cubic equations.
Rational and Radical Equations
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Equation: (x + 5)/(x - 2) = 7/3
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Solution:* x = 29/4
Rational equations require cross-multiplication to simplify the equation. -
Equation: √(5x + 2) - 3 = 1
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Solution:* x = 14/5
Shows how squaring both sides of a radical equation can isolate x. -
Equation: 2√(4x - 1) + 7 = 13
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Solution:* x = 5/2
Highlights manipulation of radicals and balancing equations.
Miscellaneous Equations
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Equation: ³√(x - 5) - 2 = 0
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Solution:* x = 13
Solving involves isolating the cube root and cubing both sides. -
Equation: 5 + 3⁴√(2x) = 11
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Solution:* x = 8
Reflects an application of root operations to isolate x. -
Equation: -3/x² + 2/x = 1/3
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Solution:* x = 3
Involves common denominators and careful algebraic manipulation. -
Equation: 2x/(x² + 5x + 4) + 3/(x + 1) = 6/(x + 4)
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Solution:* x = 6
Requires finding common denominators and algebraic restructuring to solve. -
Equation: x³ - 8x² + 16x = 0
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Solutions:* x = 0, x = 4
Factors into simpler linear components, revealing solutions directly. -
Equation: x²/8 + 1 = 3
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Solutions:* x = ±4
Demonstrates how to manipulate equations involving fractions to find values of x. -
Equation: |3x - 12| + 16 = 16
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Solution:* x = 4
Shows the effect of isolating absolute values to find solutions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of solving equations with these flashcards from Algebra II. Each card presents an equation or scenario that challenges your understanding of different solutions. Perfect for quick reviews or studying for exams!
