Give me a sample work for 02052 Algebra 1 A - 1-Variable Equations & Inequalities Apply

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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

  1. 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

  1. 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

  1. 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.