Solve This Inequality 9h 2 79

Understanding and Solving the Inequality 9h < 79

In algebra, inequalities are mathematical expressions that show a relationship where one side is greater than, less than, or not equal to the other side. The inequality 9h < 79 is a linear inequality, meaning it involves a variable raised to the first power. Solving such inequalities requires isolating the variable to determine the range of values that satisfy the condition.

Step 1: Identify the Goal

The objective is to isolate the variable h on one side of the inequality. In this case, h is being multiplied by 9, so the first step is to divide both sides by 9 to undo that multiplication.

Step 2: Perform the Division

Dividing both sides by 9 gives: [ \frac{9h}{9} < \frac{79}{9} ] Simplifying, we get: [ h < \frac{79}{9} ]

Step 3: Simplify the Fraction

The fraction 79/9 is already in its simplest form, but it can be expressed as a mixed number for better understanding: [ \frac{79}{9} = 8 \frac{7}{9} ] So, the solution can also be written as: [ h < 8 \frac{7}{9} ]

Step 4: Interpret the Solution

The solution h < 79/9 means that h can take any value less than 79/9, but not equal to or greater than it. This includes all real numbers smaller than approximately 8.78.

For more on this topic, read our article on why cell is basic unit of life or check out you are planning to move across town.

Step 5: Graphical Representation (Optional)

On a number line, this solution would be represented by an open circle at 79/9 (or 8 7/9) and a line extending to the left, indicating all values less than this point.

Common Mistakes to Avoid

• Forgetting to reverse the inequality sign when multiplying or dividing by a negative number (not applicable here since we divided by a positive 9).
• Misinterpreting the solution as a single value instead of a range.

Real-World Application

Inequalities like this are often used in real-life scenarios, such as budgeting (spending less than a certain amount) or time management (completing a task in less than a given time).

Conclusion

Solving the inequality 9h < 79 involves dividing both sides by 9 to isolate h, resulting in h < 79/9. This solution represents all real numbers less than 79/9, providing a clear range of possible values for h. Understanding how to solve such inequalities is fundamental in algebra and has practical applications in various fields.