Textbook Question
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.
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- 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
Chapter 2, Problem 17
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2
Verified step by step guidance1
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).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
Recommended video:
04:02
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.
Recommended video:
06:00Categorizing Linear Equations
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.
Recommended video:
Guided course
04:15Multiply Polynomials Using the Distributive Property
Related Practice
Textbook Question
In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x
Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x + 2
1
views
Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
Textbook Question
In Exercises 15–26, use graphs to find each set. (- 3, 0) ⋃ [- 1, 2]
1
views
Textbook Question
Find each product and write the result in standard form. (- 5 + i)(- 5 - i)