Domanda del libro di testo
Without solving the given quadratic equation, determine the number and type of solutions.
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 73
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3
Guida verificata passo dopo passo1
Start with the given equation: \(|x + 1| + 5 = 3\).
Isolate the absolute value expression by subtracting 5 from both sides: \(|x + 1| = 3 - 5\).
Simplify the right side: \(|x + 1| = -2\).
Recall that the absolute value of any expression is always greater than or equal to zero, so \(|x + 1| = -2\) has no solution because an absolute value cannot be negative.
Conclude that the equation has no solution.
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Absolute Value Definition
The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any expression |A| = B, if B is negative, there is no solution because absolute values cannot be negative.
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08:07
Vertex Form
Solving Absolute Value Equations
To solve an equation involving absolute value, isolate the absolute value expression first. Then, set up two separate equations: one where the inside expression equals the positive value, and one where it equals the negative value, solving each separately.
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5:02Solving Logarithmic Equations
Checking for No Solution
If isolating the absolute value results in a negative number on the right side, the equation has no solution. This is because absolute values cannot be negative, so no real number satisfies the equation.
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05:21Restrictions on Rational Equations
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