Textbook Question
In Exercises 9–20, find each product and write the result in standard form. (5 - 2i)2
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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 20
Solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)
Verified step by step guidance1
Start by expanding both sides of the equation: apply the distributive property to remove parentheses. For the left side, distribute 2 over (x - 1), and for the right side, distribute -3 over (x + 1). This gives you: \(2 \cdot x - 2 \cdot 1 + 3 = x - 3 \cdot x - 3 \cdot 1\).
Simplify both sides by performing the multiplications and combining like terms. On the left, simplify \(2x - 2 + 3\), and on the right, simplify \(x - 3x - 3\).
Combine like terms on each side to get a simpler linear equation. For example, combine constants on the left side and combine the \(x\) terms on the right side.
Next, get all variable terms on one side and constants on the other side. You can do this by adding or subtracting terms from both sides of the equation to isolate \(x\).
Finally, solve for \(x\) by dividing or multiplying both sides by the coefficient of \(x\). After finding the value of \(x\), substitute it back into the original equation to check if both sides are equal, confirming your solution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distributive Property
The distributive property allows you to multiply a single term by each term inside parentheses. For example, a(b + c) = ab + ac. This is essential for simplifying expressions like 2(x - 1) and -3(x + 1) before solving the equation.
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Multiply Polynomials Using the Distributive Property
Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies the equation and makes it easier to isolate the variable. For instance, terms with x can be combined to reduce complexity.
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Solving Linear Equations
Solving linear equations means finding the value of the variable that makes the equation true. This involves isolating the variable on one side using inverse operations like addition, subtraction, multiplication, or division. Checking the solution ensures accuracy.
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Related Practice
Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = - (1/2)x + 2
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Textbook Question
In Exercises 21–28, divide and express the result in standard form. 2/(3 - i)
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Textbook Question
Solve each radical equation in Exercises 11–30. Check all proposed solutions.
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Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = -(1/2)x
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
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