Podcast
Questions and Answers
In the first example, what does the linear equation $1x + 10 = 20$ represent?
In the first example, what does the linear equation $1x + 10 = 20$ represent?
- The amount of profit from selling $20 worth of apples
- The total cost of buying apples for resale
- The number of kilograms of apples sold to earn a profit of at least $20 (correct)
- The number of apples sold for $20
What is the correct method to isolate the variable in the equation $1x = 20 - 10$?
What is the correct method to isolate the variable in the equation $1x = 20 - 10$?
- Add 10 to both sides of the equation
- Divide both sides of the equation by 1
- Subtract 10 from both sides of the equation (correct)
- Multiply both sides of the equation by 1
What does the linear equation $0.75x = 15$ represent in the second example?
What does the linear equation $0.75x = 15$ represent in the second example?
- The cost of items worth $0.75 each
- The amount saved from earning $15
- The total earnings in dollars
- The amount earned for saving $15 (correct)
What is the result of dividing both sides of the equation $0.75x = 15$ by 0.75?
What is the result of dividing both sides of the equation $0.75x = 15$ by 0.75?
What does solving word problems involving linear equations in one variable entail?
What does solving word problems involving linear equations in one variable entail?
What is the significance of interpreting the solution in the context of the original problem?
What is the significance of interpreting the solution in the context of the original problem?
What is the first step in the process of solving word problems involving linear equations in one variable?
What is the first step in the process of solving word problems involving linear equations in one variable?
In the given word problem, what does the variable $$x$$ represent?
In the given word problem, what does the variable $$x$$ represent?
What does the linear equation $$1x + 10 = 20$$ represent in the given word problem?
What does the linear equation $$1x + 10 = 20$$ represent in the given word problem?
What is the second step in the process of solving word problems involving linear equations in one variable?
What is the second step in the process of solving word problems involving linear equations in one variable?
What does the fourth step in the process of solving word problems involving linear equations in one variable involve?
What does the fourth step in the process of solving word problems involving linear equations in one variable involve?
What is the simplified form of $$rac{
oot{3} ext{8}}{
oot{3} ext{2}}$$?
What is the simplified form of $$rac{ oot{3} ext{8}}{ oot{3} ext{2}}$$?
What is the third step in the process of solving word problems involving linear equations in one variable?
What is the third step in the process of solving word problems involving linear equations in one variable?
If a person travels 45 km at a constant speed of 15 km/h, how long does the journey take?
If a person travels 45 km at a constant speed of 15 km/h, how long does the journey take?
What is the value of $$rac{
oot{5} ext{32}}{
oot{5} ext{2}}$$?
What is the value of $$rac{ oot{5} ext{32}}{ oot{5} ext{2}}$$?
If an object covers a distance of 120 m in 12 seconds, what is its speed in m/s?
If an object covers a distance of 120 m in 12 seconds, what is its speed in m/s?
What is the simplified form of $$rac{
oot{4} ext{81}}{
oot{4} ext{3}}$$?
What is the simplified form of $$rac{ oot{4} ext{81}}{ oot{4} ext{3}}$$?
If a car travels at a speed of 60 km/h for 2.5 hours, how far does it travel?
If a car travels at a speed of 60 km/h for 2.5 hours, how far does it travel?
Study Notes
##Linear Equations in One Variable: Solving Word Problems
Linear equations in one variable are essential for understanding and solving real-life problems. This article will focus on the process of solving word problems involving linear equations in one variable. The general strategy to solve such problems can be broken down into the following steps:
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Read the problem: Carefully read the problem and identify the unknown quantity or quantities.
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Translate the problem into a linear equation: Transform the problem into a linear equation in the form of $$ax + b = 0$$, where $$a$$ and $$b$$ are integers, and $$x$$ is the variable.
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Solve the equation: Follow the steps to solve the linear equation, which may include isolating the variable, verifying the answer, and determining the value of the variable.
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Interpret the solution: Once the variable is determined, interpret the solution in the context of the original problem.
Let's examine some examples of word problems involving linear equations in one variable:
Example 1: A store owner wants to know how many kilograms of apples she needs to sell to earn a profit of at least $20. The cost price of each apple is $1 per kilogram. Let $$x$$ represent the number of kilograms of apples needed to earn a profit of at least $20. The equation can be written as $$1x + 10 = 20$$.
To solve this problem:
- Translate the problem into a linear equation: $$1x + 10 = 20$$.
- Isolate the variable: Subtract 10 from both sides of the equation to obtain $$1x = 20 - 10$$.
- Verify the answer: Division by 1 reveals that $$x = 20$$, which means the store owner needs to sell 20 kilograms of apples to earn a profit of at least $20.
Example 2: A person wants to save $15 for every $8 they earn. Let $$x$$ represent their earnings in dollars. The equation can be written as $$0.75x = 15$$.
To solve this problem:
- Translate the problem into a linear equation: $$0.75x = 15$$.
- Isolate the variable: Divide both sides of the equation by 0.75 to obtain $$x = 20$$.
- Verify the answer: The person needs to earn $20 to save $15.
In conclusion, solving word problems involving linear equations in one variable involves translating the problem into a linear equation, solving the equation, and interpreting the solution in the context of the original problem. By following these steps, you can effectively tackle real-life problems involving linear equations in one variable.
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Description
This article focuses on the process of solving word problems involving linear equations in one variable. It explains the steps of reading the problem, translating it into a linear equation, solving the equation, and interpreting the solution within the original problem context. Examples are provided to illustrate the application of these steps in real-life scenarios.
