Podcast
Questions and Answers
What is the solution for the equation $3(x - 3) = 3x - 6$?
What is the solution for the equation $3(x - 3) = 3x - 6$?
no solution
What is the value of b in the equation $\frac{b}{3} - 1 = 5$?
What is the value of b in the equation $\frac{b}{3} - 1 = 5$?
b = 18
What is the value of k in the equation $4k - 5k = 10 + k$?
What is the value of k in the equation $4k - 5k = 10 + k$?
k = -5
What is the value of x in the equation $6(2x + 10) = 10(x + 6)$?
What is the value of x in the equation $6(2x + 10) = 10(x + 6)$?
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What are the solutions for the equation $-2(x - 5) = 10 - 2x$?
What are the solutions for the equation $-2(x - 5) = 10 - 2x$?
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What is the solution for x in the equation $\frac{1}{5}x - \frac{2}{3} = \frac{1}{4}x + 1$?
What is the solution for x in the equation $\frac{1}{5}x - \frac{2}{3} = \frac{1}{4}x + 1$?
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If Phil, Claire, and Alex combined spend $275, how much did Phil spend if Claire spends $25 more than Phil and Alex spends half as much as Phil?
If Phil, Claire, and Alex combined spend $275, how much did Phil spend if Claire spends $25 more than Phil and Alex spends half as much as Phil?
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What are the dimensions of a rectangle with a perimeter of 82 cm, where the length is one more than three times the width?
What are the dimensions of a rectangle with a perimeter of 82 cm, where the length is one more than three times the width?
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What are three consecutive odd integers whose sum is -39?
What are three consecutive odd integers whose sum is -39?
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How old are Rob, Charles, and Kristi if the sum of their ages is 105 years and Kristi is 5 years older than Charles, while Rob is 20 years younger than twice Charles' age?
How old are Rob, Charles, and Kristi if the sum of their ages is 105 years and Kristi is 5 years older than Charles, while Rob is 20 years younger than twice Charles' age?
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Study Notes
Equations and Solutions
- No Solution: When solving 3(x - 3) = 3x - 6, the result is that there is no solution.
- Value Identification: For the equation b/3 - 1 = 5, solving gives b = 18.
- Negative Result: The equation 4k - 5k = 10 + k results in k = -5.
- Zero Solution: In the equation 6(2x + 10) = 10(x + 6), the solution yields x = 0.
- Infinite Solutions: The equation -2(x - 5) = 10 - 2x has infinite solutions, indicating all real numbers are a solution.
- Fractional Solution: For 1/5 x - 2/3 = 1/4x + 1, the resulting value of x is -100/3 or approximately -33.33.
Word Problems and Equations
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Shopping Scenario: Phil, Claire, and Alex combined spend $275. Formulating an equation from their spending habits:
- Phil = x
- Claire = x + 25
- Alex = 1/2x
- Equation: x + (x + 25) + (1/2x) = 275 leads to Phil spending $100, Claire $125, and Alex $50.
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Rectangle Perimeter: For a rectangle with a perimeter of 82 cm, with length being one more than three times the width:
- Length = 3w + 1, Width = w
- Set up the equation 2(3w + 1) + 2w = 82 leads to dimensions of width = 10 cm and length = 31 cm.
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Odd Integers Sum: The sum of three consecutive odd integers equaling -39 can be structured:
- 1st integer: x, 2nd: x + 2, 3rd: x + 4
- Equation: x + (x + 2) + (x + 4) = -39 solves to integers -15, -13, and -11.
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Siblings' Ages: For siblings Rob, Charles, and Kristi with a combined age of 105:
- Charles = x, Kristi = x + 5, Rob = 2x - 20
- Using the equation 4x - 15 = 105 results in ages: Charles = 30 years, Kristi = 35 years, Rob = 40 years.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards that cover key equations and word problems from Algebra 1 Unit 1. Each card presents a different problem to solve, helping you understand various solution types, including specific values and identities.
