Solving Using the Addition Property
To solve , the goal is to isolate by undoing the subtraction of . Apply the Addition Property of Equality by adding to both sides:
On the left side, , leaving just . On the right side, the fractions and have different denominators, so find the least common denominator (LCD) of and , which is . Rewrite as the equivalent fraction :
To verify, substitute back into the original equation:
Since is a true statement, is confirmed as the correct solution.
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Ch.2 Solving Linear Equations and Inequalities - Elementary Algebra @ OpenStax
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Solving Using the Addition Property
If , and the same number is added to both sides, which equation is true?
Arrange the steps in order to show how the Addition Property of Equality is used to solve .
To solve , you add 20 to both sides. Which property justifies this step?
Match each item with the correct part of the Addition Property of Equality.
If , what must you do after adding to ?
Adding the same number to both sides of an equation keeps the sides equal. True or False?
Adding the same number to both sides of an equation uses the _____ Property of Equality.
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Adding
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Solving Using the Addition Property
Translating and Solving 'The sum of three-eighths and is one-half'
A technician is mixing two chemical solutions. The first solution fills 1/12 of a vat, and the second fills 1/15 of the same vat. What is the Least Common Denominator (LCD) required to add these fractions?
A construction foreman is organizing various fractional lengths of steel piping. Match each pair of pipe lengths with the correct Least Common Denominator (LCD) needed to calculate their combined length.
A logistics coordinator is combining two partial shipments that represent 1/6 and 1/9 of a cargo container's capacity. True or False: The Least Common Denominator (LCD) used to add these fractions is the smallest positive number that both 6 and 9 divide into evenly.
Defining the Least Common Denominator in Technical Measurements
A logistics coordinator is combining two partial shipments that represent 1/6 and 1/8 of a cargo container's capacity. To calculate the total, the coordinator must determine the Least Common Denominator (LCD). Arrange the following steps in the correct order to find the LCD using the 'listing multiples' method.
A logistics coordinator is calculating the total warehouse space used by adding two fractional sections: 1/12 and 1/15 of the facility's total capacity. To perform this addition, the coordinator must determine the Least Common Denominator (LCD). The LCD of these fractions is defined as the ________ of the denominators 12 and 15.
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Defining the Least Common Denominator for Technical Measurements
An inventory supervisor is reconciling stock levels from two different warehouse bays. Bay 1 is at 1/12 capacity and Bay 2 is at 1/16 capacity. When preparing a combined report, the supervisor identifies 48, 96, and 144 as common denominators for these values. Which of these numbers is specifically the Least Common Denominator (LCD)?
A logistics manager is standardizing shipment data by combining loads that represent 1/15 and 1/20 of a cargo container's capacity. To add these fractions, the manager must determine the Least Common Denominator (LCD). Match each word in the term 'Least Common Denominator' with its specific mathematical role in this standardization process.
Strategy for Solving Equations with Fraction or Decimal Coefficients
Solving Using the Subtraction Property
Solving Using the Subtraction Property
Solving Using the Addition Property
Solving Using the Addition Property
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Translating and Solving 'The Difference of and is '
Solving Using the Division Property
Solving Using the Multiplication Property
Solving by Simplifying Both Sides
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Translating and Solving ' divided by is '
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Translating and Solving 'The sum of three-eighths and is one-half'
Solving by Collecting Constants
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Learn After
A logistics coordinator is calculating the initial inventory level 'x' for a specific chemical. The current balance is represented by the equation x - 5/8 = 3/4. To isolate 'x' and solve the equation using the Addition Property of Equality, what is the required first step?
A technician is calibrating a sensor where the target value 'x' minus a 5/8 unit offset equals 3/4 units, represented by the equation x - 5/8 = 3/4. To isolate 'x' and solve the equation, the technician must add the fraction ____ to both sides of the equation.
A warehouse manager is calculating the initial stock level (x) of a supply after 5/8 of a crate was used, leaving 3/4 of a crate remaining. This is modeled by the equation x - 5/8 = 3/4. Arrange the following steps in the correct order to solve for x.
A warehouse supervisor is calculating the original weight of a storage crate. After removing 5/8 of a ton of material, the remaining weight is 3/4 of a ton, represented by the equation . Match each mathematical component of the solution process with its correct role or value.
A quality control technician is calculating an initial measurement using the equation x - rac{5}{8} = rac{3}{4}. True or False: To isolate the variable on one side of the equation using the Addition Property of Equality, the technician should add to both sides of the equation.
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A logistics clerk is calculating a total shipment weight using the equation . After adding to both sides, the clerk must rewrite as an equivalent fraction with a denominator of 8 to complete the addition. Which of the following is the correct equivalent fraction?
A logistics analyst is determining the total weight capacity () of a shipping container. After a ton pallet is removed, the remaining weight is tons, which is modeled by the equation . Based on the solution process described in the course, what is the total original weight capacity ?