Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0
1
views
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 35
In Exercises 29–36, simplify and write the result in standard form. √(12 - 4 × 0.5 × 5)
Verified step by step guidance1
Start by identifying the expression inside the square root: \(1^2 - 4 \times 0.5 \times 5\). This is the discriminant of a quadratic equation, but here we are simply simplifying it.
Simplify \(1^2\). Recall that \(1^2 = 1\).
Simplify the product \(4 \times 0.5 \times 5\). Multiply these numbers step by step: first \(4 \times 0.5\), then multiply the result by \(5\).
Subtract the result of \(4 \times 0.5 \times 5\) from \(1\). This gives the value inside the square root.
Finally, take the square root of the resulting value. If the value inside the square root is negative, the result will involve imaginary numbers, and you should express it in terms of \(i\), where \(i = \sqrt{-1}\).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. In this context, the expression involves calculating the square root of a result derived from a mathematical operation. Understanding how to simplify square roots is essential for solving the problem.
Recommended video:
02:20
Imaginary Roots with the Square Root Property
Order of Operations
Order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Applying these rules correctly is crucial for simplifying the expression accurately.
Recommended video:
Guided course
8:38Performing Row Operations on Matrices
Standard Form
Standard form in mathematics typically refers to expressing numbers in a conventional way, such as writing a polynomial in descending order of its degree or representing complex numbers in the form a + bi. In this exercise, simplifying the expression to standard form means presenting the final result clearly and concisely, which is important for clarity in mathematical communication.
Recommended video:
Guided course
05:16Standard Form of Polynomials
Related Practice
Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (2x + 8)2 = 27
Textbook Question
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
Textbook Question
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4
Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(x + 1) + 2 ≥ 3x + 6
Textbook Question
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R