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Including a 10.5% hotel tax, your room in San Diego cost \$216.58 per night. Find the nightly cost before the tax was added.
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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 17
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2
Guida verificata passo dopo passo1
Start by expanding the left side of the equation using the distributive property: \(7(x - 4) = 7 \cdot x - 7 \cdot 4\) which simplifies to \(7x - 28\).
Rewrite the equation with the expanded left side: \(7x - 28 = x + 2\).
Next, get all the variable terms on one side and the constants on the other side. Subtract \(x\) from both sides to isolate the variable terms: \(7x - x - 28 = 2\) which simplifies to \(6x - 28 = 2\).
Then, add 28 to both sides to move the constant term: \(6x - 28 + 28 = 2 + 28\) which simplifies to \(6x = 30\).
Finally, solve for \(x\) by dividing both sides by 6: \(x = \frac{30}{6}\). After finding \(x\), analyze the solution to determine if the equation is an identity (true for all \(x\)), a conditional equation (true for specific \(x\)), or inconsistent (no solution).
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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, and division. The goal is to find the value of the variable that makes the equation true.
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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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Distributive Property
The distributive property allows you to multiply a single term by each term inside parentheses, e.g., a(b + c) = ab + ac. This property is essential for simplifying expressions before solving equations.
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