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Plot the given point in a rectangular coordinate system. (- 4, 0)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 2, Problema 9
Solve and check each linear equation. x - 5(x + 3) = 13
Guida verificata passo dopo passo1
Distribute the -5 across the terms inside the parentheses: \( x - 5(x + 3) = x - 5x - 15 \).
Combine like terms on the left side of the equation: \( x - 5x - 15 = -4x - 15 \).
Set the equation equal to 13: \( -4x - 15 = 13 \).
Add 15 to both sides to isolate the term with \( x \): \( -4x = 13 + 15 \).
Divide both sides by -4 to solve for \( x \): \( x = \frac{28}{-4} \).
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Linear Equations
A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving a linear equation involves isolating the variable on one side of the equation to find its value.
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Categorizing Linear Equations
Distributive Property
The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by two or more terms inside parentheses. This property is essential for simplifying expressions and solving equations, as it helps eliminate parentheses and combine like terms effectively.
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04:15Multiply Polynomials Using the Distributive Property
Checking Solutions
Checking solutions involves substituting the found value of the variable back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation, confirming that no errors occurred during the solving process. It is a crucial part of problem-solving in algebra.
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05:21Restrictions on Rational Equations
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