Algebra 1A - Unit 2: Lines and Their Graphs
14 Questions
101 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is lesson 6 about?

  • Solving Linear Equations (correct)
  • Graphing Quadratic Functions
  • Factoring Polynomials
  • Calculating Probabilities

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?

<p>t = 29</p> Signup and view all the answers

Match each equation with the correct value of t that makes the equation true.

<p>3t - 1/4 = 0.75 = t = 1/3 -2/5t + 6 = 14 = t = -20 t + 0.5/2 = 7.25 = t = 14 t ÷ 9 + 5 = 50 = t = 405</p> Signup and view all the answers

Which equations represent the situation where Ezgi's mom bought tickets and snacks for her birthday?

<p>6s + 75 = 105 (A), 6(s + 75) = 105 (C)</p> Signup and view all the answers

Which equations represent the chaperone situation in the school field trip?

<p>10c = 113 (A), c = 113/10 (B)</p> Signup and view all the answers

In the equation y = 2.4x, the variable y is the independent variable.

<p>False (B)</p> Signup and view all the answers

The solution b = 6 from the equation 18.60 = 2.60b + 3 gives the number of miles the taxi traveled.

<p>True (A)</p> Signup and view all the answers

How much was each game ticket if Leo and Bonnie paid $70.50 total for tickets and jerseys?

<p>$20.25</p> Signup and view all the answers

Tim's solution of 8.5 students for Mr. Khan's class is reasonable.

<p>False (B)</p> Signup and view all the answers

Sermet's solution of h = 180 hours is reasonable for earning money in a week.

<p>False (B)</p> Signup and view all the answers

What is the equation for the population of Smallville to reach 2282?

<p>2282 = 12(7420 − 152x) − 1200</p> Signup and view all the answers

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?

<p>280 = s + 2s + (s + 20)</p> Signup and view all the answers

Flashcards

Linear Equation

A mathematical statement that shows the equality of two expressions, often involving variables.

Solution to an Equation

The value of the variable that makes the equation true, like finding the missing piece of a puzzle.

Division Property of Equality

Performing the same operation on both sides of an equation to maintain equality, like balancing a scale by adding or removing weights on both sides.

Steps to Solve Equations

A step-by-step process to isolate the variable and find its solution, like unraveling a mystery.

Signup and view all the flashcards

Solving for a Variable

Using the properties of equality to isolate the variable, like finding the hidden treasure in a riddle.

Signup and view all the flashcards

Matching Equations with Solutions

The process of matching equations with their corresponding solutions, like finding matching pairs.

Signup and view all the flashcards

Real-World Applications of Equations

A way to represent real-life situations using equations and then solve for the unknown, like decoding a real-world problem.

Signup and view all the flashcards

Variable

A symbol used to represent an unknown quantity, like a blank space in a story.

Signup and view all the flashcards

Equation as a Relationship

A representation of a relationship between quantities, like mapping a journey.

Signup and view all the flashcards

Solving Equations with Real-World Values

Solving an equation by substituting real-world values to find the unknown quantity, like applying the map to find the destination.

Signup and view all the flashcards

Verifying Solutions

The process of checking if the solution found satisfies the conditions of the problem, like confirming the treasure is the right one.

Signup and view all the flashcards

Applying Equations to Real-World Scenarios

The process of representing real-life situations using equations and then interpreting the solution in context, like understanding the journey's meaning.

Signup and view all the flashcards

Linear Equation

A type of equation with variables that only have exponents of 1, like a straight line.

Signup and view all the flashcards

Solving Real-World Problems with Equations

A process of finding the unknown value in an equation that represents a real-world problem.

Signup and view all the flashcards

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

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

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.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser