Textbook Question
If 5 times a number is decreased by 4, the principal square root of this difference is 2 less than the number. Find the number(s).
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 106a
Solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]
Verified step by step guidance1
Distribute the -2 inside the parentheses on the left-hand side: -2(1 - x) becomes -2 + 2x. Simplify the expression inside the brackets.
Simplify the brackets on the left-hand side: [4 - (-2 + 2x) + 3] becomes [4 + 2 - 2x + 3]. Combine like terms inside the brackets.
Simplify further on the left-hand side: [4 + 2 + 3 - 2x] becomes [9 - 2x]. Multiply the entire bracket by -2.
On the right-hand side, distribute the -2 inside the parentheses: -2(x - 3) becomes -2x + 6. Simplify the expression inside the brackets.
Combine all terms on both sides of the equation, isolate x, and solve for x by performing inverse operations (addition, subtraction, division, etc.).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Order of Operations
The 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. In solving equations, correctly applying these rules is crucial for simplifying expressions accurately.
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Performing Row Operations on Matrices
Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a set of parentheses. This property is essential for simplifying expressions and solving equations, as it helps eliminate parentheses and combine like terms effectively, making the equation easier to manage.
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04:15Multiply Polynomials Using the Distributive Property
Solving Linear Equations
Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes isolating the variable on one side of the equation through various algebraic manipulations, such as adding, subtracting, multiplying, or dividing both sides. Understanding how to manipulate equations is fundamental for arriving at the correct solution.
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04:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4
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Textbook Question
In Exercises 107–110, use graphs to find each set. (-2,1] ∩ [-1,3)
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Textbook Question
When 3 times a number is subtracted from 4, the absolute value of the difference is at least 5. Use interval notation to express the set of all numbers that satisfy this condition.
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Textbook Question
Use the table to solve each inequality. - 3 < 2x - 5 ≤ 3
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Textbook Question
Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)
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