Questions and Answers
What is lesson 6 about?
What value of x makes the equation 6x = 3/22 true?
1/44
What property did Klara use in step 2 of her solution for the equation −5x − 8 = 32?
Division Property of Equality
What method correctly solves the equation 2(t − 5) = 48?
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Match each equation with the correct value of t that makes the equation true.
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Which equations represent the situation where Ezgi's mom bought tickets and snacks for her birthday?
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Which equations represent the chaperone situation in the school field trip?
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In the equation y = 2.4x, the variable y is the independent variable.
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The solution b = 6 from the equation 18.60 = 2.60b + 3 gives the number of miles the taxi traveled.
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How much was each game ticket if Leo and Bonnie paid $70.50 total for tickets and jerseys?
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Tim's solution of 8.5 students for Mr. Khan's class is reasonable.
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Sermet's solution of h = 180 hours is reasonable for earning money in a week.
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What is the equation for the population of Smallville to reach 2282?
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Each day, a factory produces a total of 280 containers of ice cream. If s represents the number of containers of strawberry ice cream produced per day, what is the correct equation?
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Study Notes
Solving Linear Equations
- Lesson focuses on methods for solving linear equations.
Values and Equations
- The equation (6x = \frac{3}{22}) yields (x = \frac{1}{44}).
Properties of Equations
- Klara applies the division property of equality to transition from (-5x = 40) to (x = -8x).
Steps to Solve Equations
- For (2(t - 5) = 48), the solution involves dividing both sides by 2, leading to (t - 5 = 24) and solving to find (t = 29).
Matching Equations with Solutions
- Equations matched with values:
- (3t - \frac{1}{4} = 0.75) gives (t = \frac{1}{3}).
- (-\frac{2}{5}t + 6 = 14) gives (t = -20).
- (t + \frac{0.5}{2} = 7.25) gives (t = 14).
- (t \div 9 + 5 = 50) gives (t = 405).
Real-World Applications
- Egzi's birthday scenario involves a total cost equation of (6s + 75 = 105) or (6(s + 75) = 105) where (s) is the snack cost.
- For a school field trip, the chaperone equation is represented by (10c = 113) or (c = \frac{113}{10}).
Understanding Variables
- In the equation (y = 2.4x), (y) reflects the meters run and (x) represents time in seconds.
Taxi Fare Calculation
- Alex's total taxi fare scenario translates to (18.60 = 2.60b + 3) where (b) indicates miles traveled, here (b = 6).
Ticket Pricing
- For a basketball game ticket and jersey costing (70.50), each ticket is (20.25).
Analyzing Class Sizes
- In a situation with Mr. Mauldin and Mrs. Sasser, the equation (35 = 2(9 + k)) is accurate, but (k = 8.5) is unreasonable as students cannot be half.
Financial Planning
- Sermet's equation (3250 = 12.5h + 1000) leads to (h = 180), which is impractical due to only having 168 available hours in a week.
Population Dynamics
- Smallville's population will be calculated with (2282 = \frac{1}{2}(7420 - 152x) - 1200), predicting it will reach (2282) in 3 years.
Ice Cream Production Problem
- The factory produces 280 containers of ice cream daily with specific ratios between flavors; the correct total produced by each flavor needs further elaboration for complete equations and solutions.
Studying That Suits You
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Description
Test your knowledge of linear equations with these flashcards from Algebra 1A - Unit 2. This quiz covers solving linear equations, understanding properties of equality, and more. Perfect for reinforcing your understanding of lines and their graphs.
