Here's a sample work project based on Algebra 1 concepts, specifically focusing on one-variable equations and inequalities. This project includes explanations and examples that align with the typical curriculum for Algebra 1.
Algebra 1A Project: 1-Variable Equations & Inequalities
Objective:
To practice solving and applying one-variable equations and inequalities in real-life scenarios.
Instructions:
Complete the following tasks and problems. Show all calculations and reasoning for full credit.
Part 1: Solving One-Variable Equations
-
Equation Solving Practice: Solve the following equations:
a) \( 3x + 5 = 20 \)
b) \( 2(x - 4) = 12 \)
c) \( 7 - 2x = 1 \)
d) \( 4x + 1 = 3x + 6 \)
Solutions:
a) \[ 3x + 5 = 20 \] Subtract 5 from both sides: \[ 3x = 15 \] Divide both sides by 3: \[ x = 5 \]
b) \[ 2(x - 4) = 12 \] Divide both sides by 2: \[ x - 4 = 6 \] Add 4 to both sides: \[ x = 10 \]
c) \[ 7 - 2x = 1 \] Subtract 7 from both sides: \[ -2x = -6 \] Divide by -2: \[ x = 3 \]
d) \[ 4x + 1 = 3x + 6 \] Subtract 3x from both sides: \[ x + 1 = 6 \] Subtract 1 from both sides: \[ x = 5 \]
Part 2: Solving One-Variable Inequalities
-
Inequality Solving Practice: Solve the following inequalities:
a) \( 2x - 3 < 5 \)
b) \( -4x + 1 \geq 13 \)
c) \( 5 - 2x \leq 3 \)
d) \( 3x + 4 > 10 \)
Solutions:
a) \[ 2x - 3 < 5 \] Add 3 to both sides: \[ 2x < 8 \] Divide by 2: \[ x < 4 \]
b) \[ -4x + 1 \geq 13 \] Subtract 1 from both sides: \[ -4x \geq 12 \] Divide by -4 (remember to flip the inequality): \[ x \leq -3 \]
c) \[ 5 - 2x \leq 3 \] Subtract 5 from both sides: \[ -2x \leq -2 \] Divide by -2 (flip the inequality): \[ x \geq 1 \]
d) \[ 3x + 4 > 10 \] Subtract 4 from both sides: \[ 3x > 6 \] Divide by 3: \[ x > 2 \]
Part 3: Real-Life Application
-
Application Problem: Imagine you are buying tickets for a concert. Each ticket costs $15. You have a budget of $120.
a) Write an inequality that represents the situation.
b) Solve the inequality to determine the maximum number of tickets you can buy.
Solution:
a) Let \( x \) be the number of tickets. The inequality can be represented as: \[ 15x \leq 120 \]
b) To find the maximum number of tickets: \[ x \leq \frac{120}{15} \] \[ x \leq 8 \]
So, you can buy a maximum of 8 tickets.
Conclusion:
Review your solutions to ensure accuracy, and be prepared to discuss any questions you might have on equations and inequalities.
Submission:
Submit your completed work to your teacher by the due date.
This serves as a well-rounded practice to reinforce skills in one-variable equations and inequalities, including both theory and application.