Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0
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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 34
A job pays an annual salary of \$57,900, which includes a holiday bonus of \$1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?
Verified step by step guidance1
First, determine the total annual salary excluding the holiday bonus by subtracting the bonus from the total salary: \(\$57,900 - \$1,500\).
Next, calculate the number of paychecks issued in a year. Since paychecks are issued twice a month, multiply the number of months in a year by 2: \(12 \times 2\).
Then, divide the adjusted annual salary (total salary minus bonus) by the number of paychecks to find the gross amount for each regular paycheck: \(\frac{\text{Adjusted Annual Salary}}{\text{Number of Paychecks}}\).
After that, consider how the holiday bonus is paid. If it is included in the total annual salary, decide whether it is distributed evenly across all paychecks or paid separately. For this problem, since the bonus is included, it is likely distributed evenly.
Finally, calculate the gross amount for each paycheck by dividing the total annual salary (including the bonus) by the number of paychecks: \(\frac{\$57,900}{24}\). This gives the gross amount for each paycheck.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Annual Salary and Components
The annual salary is the total amount earned in one year, including all bonuses and additional pay. Understanding that the holiday bonus is part of the total $57,900 helps in calculating the regular pay portion separately if needed.
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Pay Periods and Frequency
Paychecks issued twice a month means there are 24 pay periods in a year (2 per month × 12 months). Knowing the number of pay periods is essential to divide the annual salary correctly to find the gross amount per paycheck.
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Gross Pay Calculation
Gross pay is the total earnings before deductions. To find the gross amount per paycheck, divide the total annual salary by the number of pay periods. This calculation provides the paycheck amount before taxes or other withholdings.
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Related Practice
Textbook Question
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - x = x/10 - 5/2
Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (2x + 8)2 = 27
Textbook Question
For an international telephone call, a telephone company charges \$0.43 for the first minute, \$0.32 for each additional minute, and a \$2.10 service charge. If the cost of a call is \$5.73, how long did the person talk?
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Textbook Question
In Exercises 29–36, simplify and write the result in standard form. √(32 - 4 × 2 × 5)
Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(x + 1) + 2 ≥ 3x + 6