tyson wants to solve the inequality

2 min read 06-03-2025

Tyson Tackles Inequalities: Solving x + 3 > 7

Tyson's got a math problem! He needs to solve the inequality x + 3 > 7. Let's walk through how to help him find the solution. This is a great example of a simple linear inequality, a fundamental concept in algebra.

Understanding Inequalities

Before we dive in, let's refresh what inequalities are. Unlike equations, which use an equals sign (=), inequalities use symbols like:

> (greater than)
< (less than)
≥ (greater than or equal to)
≤ (less than or equal to)

These symbols show the relationship between two expressions. In Tyson's problem, x + 3 > 7 means "x plus 3 is greater than 7."

Solving x + 3 > 7: Step-by-Step

Solving inequalities is similar to solving equations, but with one crucial difference: when you multiply or divide by a negative number, you must flip the inequality sign. Let's solve Tyson's problem step-by-step:

Isolate the variable: Our goal is to get 'x' by itself on one side of the inequality. To do this, we subtract 3 from both sides:

x + 3 - 3 > 7 - 3
Simplify: This simplifies to:

x > 4

That's it! Tyson's solution is x > 4. This means any value of 'x' greater than 4 will make the original inequality x + 3 > 7 true.

Checking the Solution

Let's test a few values to verify our solution:

x = 5: 5 + 3 = 8, and 8 > 7. This is true!
x = 4: 4 + 3 = 7, and 7 is not greater than 7. This is false.
x = 3: 3 + 3 = 6, and 6 is not greater than 7. This is false.

These examples confirm that our solution, x > 4, is correct. Any number greater than 4 will satisfy the inequality.

Representing the Solution

We can represent the solution graphically on a number line. We'll use an open circle at 4 (because x is greater than, not greater than or equal to, 4) and shade the line to the right, indicating all values greater than 4.

[Insert image here: A number line with an open circle at 4 and the line shaded to the right.] (Alt Text: Number line showing the solution to x > 4)

What if the Inequality was Different?

Let's consider a slightly different problem: x - 5 ≤ 2

Add 5 to both sides: x - 5 + 5 ≤ 2 + 5
Simplify: x ≤ 7

In this case, the solution is x ≤ 7, meaning x can be 7 or any number less than 7. On a number line, we'd use a closed circle at 7 (because it's included) and shade to the left.

[Insert image here: A number line with a closed circle at 7 and the line shaded to the left.] (Alt Text: Number line showing the solution to x ≤ 7)

Conclusion

Solving inequalities is a crucial skill in algebra. By following these steps and understanding the rules, Tyson (and you!) can confidently tackle any inequality problem. Remember to isolate the variable and, importantly, flip the inequality sign when multiplying or dividing by a negative number. Now Tyson is ready to conquer more complex inequalities!