Textbook Question
In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7
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 74
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x
Verified step by step guidance1
Start by expanding the left side of the equation using the distributive property: \(4(x + 5) = 4 \times x + 4 \times 5\).
Rewrite the equation after distribution: \(4x + 20 = 21 + 4x\).
Next, subtract \$4x$ from both sides to begin isolating the constants: \(4x + 20 - 4x = 21 + 4x - 4x\).
Simplify both sides: \(20 = 21\).
Analyze the resulting statement: since \(20 = 21\) is false, conclude whether the equation is an identity, conditional, or inconsistent based on this contradiction.
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 simplifying 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
Solve each equation in Exercises 65–74 using the quadratic formula. x2 - 6x + 10 = 0
Textbook Question
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair (2, 5) satisfies 3y - 2x = - 4.
Textbook Question
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
1
views
Textbook Question
Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8
1
views
Textbook Question
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
5
views