Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |(2x + 2)/4| ≥ 2
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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 75
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3
Guida verificata passo dopo passo1
Start by writing down the given equation: \(10x + 3 = 8x + 3\).
To isolate the variable terms on one side, subtract \$8x$ from both sides: \(10x + 3 - 8x = 8x + 3 - 8x\), which simplifies to \(2x + 3 = 3\).
Next, subtract 3 from both sides to isolate the term with \(x\): \(2x + 3 - 3 = 3 - 3\), which simplifies to \(2x = 0\).
Now, solve for \(x\) by dividing both sides by 2: \(\frac{2x}{2} = \frac{0}{2}\), which simplifies to \(x = 0\).
Finally, analyze the solution: since you found a specific value for \(x\), the equation is a conditional equation (true only for \(x = 0\)).
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Solving Linear Equations
Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. The goal is to find the value of the variable that makes the equation true.
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Solving Linear Equations with Fractions
Types of Equations: Identity, Conditional, and Inconsistent
An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. Identifying the type depends on the solution set after solving the equation.
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Properties of Equality
Properties of equality, such as the addition, subtraction, multiplication, and division properties, allow manipulation of equations without changing their solutions. These properties are essential for maintaining balance while solving equations.
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