Textbook Question
Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.
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Ch. 1 - Equations and Inequalities
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 2, Problem 5
Solve each problem. If 120 L of an acid solution is 75% acid, how much pure acid is there in the mixture?
Verified step by step guidance1
Identify the total volume of the acid solution, which is 120 liters, and the concentration of acid in the solution, which is 75%.
Convert the percentage concentration to a decimal by dividing 75 by 100, so 75% becomes 0.75.
Set up the expression to find the amount of pure acid by multiplying the total volume by the decimal concentration: \(120 \times 0.75\).
Perform the multiplication to find the volume of pure acid in liters (do not calculate the final number yet).
Interpret the result as the amount of pure acid present in the 120 liters of solution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentage Concentration
Percentage concentration expresses the amount of a substance in a mixture as a percent of the total mixture. In this problem, 75% acid means that 75 parts out of every 100 parts of the solution are pure acid.
Volume Calculation
Volume calculation involves determining the quantity of a component within a mixture. Here, you multiply the total volume of the solution by the percentage (in decimal form) to find the volume of pure acid.
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Conversion of Percentage to Decimal
To perform calculations with percentages, convert the percentage to a decimal by dividing by 100. For example, 75% becomes 0.75, which can then be multiplied by the total volume to find the amount of pure acid.
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