Question

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

Answer 1

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.

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### 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.

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#### 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

2. **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

3. **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.

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#### 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.

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This serves as a well-rounded practice to reinforce skills in one-variable equations and inequalities, including both theory and application.