Algebra 1 Inequalities Practice Worksheet with Solutions

Mastering Algebra 1 Inequalities: A Practice Worksheet with Solutions

Algebra 1 inequalities are a fundamental concept in mathematics, and mastering them is crucial for success in higher-level math courses. In this practice worksheet, we will provide you with a series of inequality problems, along with detailed solutions to help you understand the concepts better.

Solving Linear Inequalities

Linear inequalities are inequalities that can be written in the form ax + b > 0, where a and b are constants. To solve linear inequalities, we need to isolate the variable (usually x) on one side of the inequality sign.

Example 1: Solve the inequality 2x + 5 > 3.

📝 Note: To solve this inequality, we need to isolate x by subtracting 5 from both sides and then dividing both sides by 2.

Solution:

2x + 5 > 3

Subtract 5 from both sides:

2x > -2

Divide both sides by 2:

x > -1

Example 2: Solve the inequality x - 3 ≤ 2.

📝 Note: To solve this inequality, we need to add 3 to both sides and then divide both sides by 1 (since the coefficient of x is 1).

Solution:

x - 3 ≤ 2

Add 3 to both sides:

x ≤ 5

Solving Compound Inequalities

Compound inequalities are inequalities that involve two or more inequality signs. To solve compound inequalities, we need to solve each inequality separately and then combine the solutions.

Example 3: Solve the compound inequality -2 ≤ x < 5.

📝 Note: To solve this compound inequality, we need to solve each inequality separately and then combine the solutions.

Solution:

-2 ≤ x (solve by adding 2 to both sides)

x ≥ -2

x < 5 (solve by subtracting 5 from both sides)

x < 5

Combine the solutions:

-2 ≤ x < 5

Solving Absolute Value Inequalities

Absolute value inequalities involve the absolute value of an expression. To solve absolute value inequalities, we need to consider two cases: one where the expression is positive, and one where the expression is negative.

Example 4: Solve the absolute value inequality |x - 2| > 3.

📝 Note: To solve this absolute value inequality, we need to consider two cases: x - 2 > 3 and x - 2 < -3.

Solution:

Case 1: x - 2 > 3

x > 5

Case 2: x - 2 < -3

x < -1

Combine the solutions:

x < -1 or x > 5

Practice Problems

Now it’s your turn to practice solving inequalities! Try to solve the following problems on your own, and then check your answers with the solutions provided below.

1. Solve the inequality x + 2 > 7.
2. Solve the compound inequality -3 < x ≤ 2.
3. Solve the absolute value inequality |2x + 1| ≤ 5.

Solutions

1. x > 5
2. -3 < x ≤ 2
3. -3 ≤ x ≤ 2

Tips and Tricks

• When solving inequalities, make sure to isolate the variable on one side of the inequality sign.
• When solving compound inequalities, solve each inequality separately and then combine the solutions.
• When solving absolute value inequalities, consider two cases: one where the expression is positive, and one where the expression is negative.
• Always check your solutions by plugging them back into the original inequality.

Conclusion

In this practice worksheet, we covered the basics of solving linear, compound, and absolute value inequalities. By mastering these concepts, you’ll be well-prepared to tackle more advanced math topics. Remember to always isolate the variable, solve each inequality separately, and consider multiple cases when necessary.

Related Terms:

• Algebra 1 Inequalities Worksheet pdf
• Inequalities Worksheet with answers
• Inequalities Worksheet PDF with answers
• One-Step Inequalities Worksheet PDF
• Solving Inequalities Worksheet PDF
• Compound inequalities worksheet