Domanda del libro di testo
In Exercises 81–85, use a calculator's factorial key to evaluate each expression.
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Ch. 8 - Sequences, Induction, and Probability
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 9, Problema 86
Solve: .
Guida verificata passo dopo passo1
Start by isolating the absolute value expression. Add 7 to both sides of the equation: 6|1 – 2x| – 7 + 7 = 11 + 7, which simplifies to 6|1 – 2x| = 18.
Next, divide both sides of the equation by 6 to solve for the absolute value: |1 – 2x| = 18 / 6, which simplifies to |1 – 2x| = 3.
Recall that the absolute value equation |A| = B means A = B or A = -B. So, set up two separate equations: 1 – 2x = 3 and 1 – 2x = -3.
Solve each equation for x separately. For 1 – 2x = 3, subtract 1 from both sides and then divide by -2. For 1 – 2x = -3, subtract 1 from both sides and then divide by -2.
Write the two solutions for x obtained from the previous step. These are the values of x that satisfy the original equation.
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Absolute Value Equations
An absolute value equation involves expressions within absolute value bars, which represent the distance from zero on the number line. To solve such equations, set the expression inside the absolute value equal to both the positive and negative values of the number on the other side of the equation.
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Categorizing Linear Equations
Isolating the Absolute Value Expression
Before solving an absolute value equation, isolate the absolute value term on one side of the equation. This often involves performing inverse operations like addition, subtraction, multiplication, or division to simplify the equation and make the absolute value expression alone.
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Solving Linear Equations
After splitting the absolute value equation into two cases, solve each resulting linear equation by isolating the variable. This includes applying inverse operations and simplifying to find the values of the variable that satisfy the original equation.
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04:02Solving Linear Equations with Fractions
Pratica correlata
Domanda del libro di testo
Exercises 88–90 will help you prepare for the material covered in the next section. Consider the sequence 1, −2, 4, −8, 16, ………. Find a2/a3, a1/a2, a4/a3 and a5/a4 What do you observe?
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Domanda del libro di testo
Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.
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Domanda del libro di testo
Use a calculator's factorial key to evaluate each expression. 20!/(20−3)!
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Domanda del libro di testo
Graph: f(x) = -2(x − 1)² (x + 3).
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Domanda del libro di testo
Solve: log2 (x+9) — log2 x = 1.
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