Algebra 1A - Unit 2: Lines and Their Graphs

What is lesson 6 about?

What value of x makes the equation 6x = 3/22 true?

What property did Klara use in step 2 of her solution for the equation −5x − 8 = 32?

What method correctly solves the equation 2(t − 5) = 48?

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

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

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

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

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

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

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

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

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

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?

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.

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.