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 33
In Exercises 29–36, simplify and write the result in standard form. √(32 - 4 × 2 × 5)
Verified step by step guidance1
Start by simplifying the expression inside the square root. The expression is 3^2 - 4 × 2 × 5. First, calculate 3^2, which means 3 raised to the power of 2.
Next, calculate the product of 4, 2, and 5. Multiply these numbers together to simplify the second term inside the square root.
Subtract the result of the multiplication (4 × 2 × 5) from the result of 3^2. This will simplify the expression inside the square root to a single value.
Now, take the square root of the simplified value obtained in the previous step. Ensure that the value inside the square root is non-negative, as square roots of negative numbers are not real numbers.
Finally, write the result in standard form. If the square root simplifies to an integer, write the integer. If it does not simplify completely, leave it in simplified radical form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root
The square root of a number is a value that, when multiplied by itself, gives the original number. In this problem, we need to simplify the expression under the square root before calculating its value. The square root is denoted by the radical symbol (√) and is fundamental in algebra for solving equations and simplifying expressions.
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Order of Operations
Order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In this exercise, correctly applying these rules is crucial for simplifying the expression under the square root accurately.
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Standard Form
Standard form in mathematics typically refers to a way of writing numbers or expressions in a conventional format. For complex numbers, it is expressed as a + bi, where a and b are real numbers and i is the imaginary unit. In this context, simplifying the expression to standard form means presenting the final result clearly and concisely, which is essential for clarity in mathematical communication.
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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
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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. 8x - 11 ≤ 3x - 13
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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
A repair bill on a sailboat came to \$2356, including \$826 for parts and the remainder for labor. If the cost of labor is \$90 per hour, how many hours of labor did it take to repair the sailboat?
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Textbook Question
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)3/2 = 27
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