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Ch. R - Algebra Review
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. R - Algebra ReviewProblema 11
Capitolo 1, Problema 11

Solve each linear equation. See Examples 1–3. 7x + 8 = 1

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Identify the given linear equation: \(7x + 8 = 1\).
Isolate the term containing \(x\) by subtracting 8 from both sides: \(7x + 8 - 8 = 1 - 8\) which simplifies to \(7x = 1 - 8\).
Simplify the right side of the equation: \(7x = -7\).
Solve for \(x\) by dividing both sides by 7: \(x = \frac{-7}{7}\).
Simplify the fraction to find the value of \(x\).

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Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. It represents a straight line when graphed. Solving a linear equation involves finding the value of the variable that makes the equation true.
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Categorizing Linear Equations

Isolating the Variable

Isolating the variable means manipulating the equation to get the variable alone on one side. This typically involves performing inverse operations such as addition, subtraction, multiplication, or division to both sides of the equation to maintain equality.
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Equations with Two Variables

Properties of Equality

Properties of equality state that you can add, subtract, multiply, or divide both sides of an equation by the same nonzero number without changing the equation's solution. These properties are essential for maintaining balance while solving equations.
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Imaginary Roots with the Square Root Property
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For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2. P(-5, -6), Q(7, -1)

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Find each sum or difference. See Example 1. -6 + (-13)

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Find the domain of each rational expression. See Example 1. (x + 3) / (x - 6)

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Find each square root. See Example 1. √100

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List the elements in each set. See Example 1. {z|z is a natural number greater than 4}

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For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the midpoint M of line segment PQ. See Examples 1 and 2.

P(8, 2), Q(3, 5)

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