What is Solving an Inequality?

S3-SA1-0052

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Solving an inequality means finding all the values for a variable that make the inequality true. It's like finding a range of numbers that fit a certain condition, instead of just one exact number as in an equation.

Simple Example

Quick Example

Imagine your school says you need to score 'more than 70 marks' in your maths exam to get an A grade. This is an inequality. If 'M' is your marks, then M > 70. Solving this means any marks like 71, 72, 85, or 100 will get you an A grade.

Worked Example

Step-by-Step

Let's solve the inequality: x + 3 < 10

1. Our goal is to get 'x' by itself on one side, just like in an equation.
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2. To remove '+ 3' from the left side, we subtract 3 from both sides of the inequality.
x + 3 - 3 < 10 - 3
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3. Simplify both sides.
x < 7
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4. The solution is x < 7. This means any number less than 7 (like 6, 5, 0, -2, etc.) will make the original inequality true.
Answer: x < 7

Why It Matters

Understanding inequalities helps in fields like AI/ML to set boundaries for data, in Physics to describe ranges of motion, and in Economics to model budget constraints. Engineers use them to design systems that operate within safe limits, and even data scientists use them to filter information.

Common Mistakes

MISTAKE: Treating inequalities exactly like equations when multiplying or dividing by a negative number. | CORRECTION: Remember to FLIP the inequality sign (from < to > or vice versa) if you multiply or divide both sides by a negative number.

MISTAKE: Forgetting that 'greater than or equal to' (>=) includes the number itself. | CORRECTION: If the sign is >= or <=, the solution set includes the boundary number. For example, x >= 5 includes 5, 6, 7...

MISTAKE: Not checking the answer with a value from the solution set. | CORRECTION: Pick a number that you think is in your solution set and substitute it back into the original inequality to see if it holds true.

Practice Questions

Try It Yourself

QUESTION: Solve: y - 5 > 8 | ANSWER: y > 13

QUESTION: Solve: 2x <= 14 | ANSWER: x <= 7

QUESTION: Solve: -3z + 1 < 10 | ANSWER: z > -3

MCQ

Quick Quiz

Which of the following numbers is NOT a solution to the inequality x + 4 > 9?

The Correct Answer Is:

Solving x + 4 > 9 gives x > 5. This means any number greater than 5 is a solution. 5 itself is not greater than 5, so it's not a solution.

Real World Connection

In the Real World

When you buy mobile data, your plan might say 'You have less than 1 GB data remaining' (Data < 1 GB). Or when you book a train ticket, there might be 'more than 10 seats available' (Seats > 10). These are everyday inequalities we solve without even thinking about it, helping us make decisions.

Key Vocabulary

Key Terms

INEQUALITY: A mathematical statement comparing two expressions using signs like <, >, <=, >=. | VARIABLE: A letter (like x, y) representing an unknown number. | SOLUTION SET: All the values that make an inequality true. | FLIP THE SIGN: Changing < to > or vice versa when multiplying/dividing by a negative number.

What's Next

What to Learn Next

Great job learning about solving basic inequalities! Next, you can explore how to solve inequalities with variables on both sides, or even how to graph inequalities on a number line. These next steps will help you visualize and understand more complex problems.