Answer :
- Add 15 to both sides of the inequality.
- Simplify the inequality to isolate $x$.
- The solution is $x < 40$.
- The correct option is $x<40$.
### Explanation
1. Understanding the Problem
We are asked to solve the inequality $x - 15 < 25$ for $x$. This means we want to find all values of $x$ that make the inequality true.
2. Isolating x
To isolate $x$, we need to get rid of the $-15$ on the left side of the inequality. We can do this by adding $15$ to both sides of the inequality:$$x - 15 + 15 < 25 + 15$$
3. Simplifying the Inequality
Now, we simplify both sides of the inequality:$$x < 40$$This means that any value of $x$ that is less than $40$ will satisfy the original inequality.
4. Finding the Correct Option
Comparing our solution $x < 40$ with the given options, we find that the correct answer is $x<40$.
### Examples
Understanding inequalities like this helps in everyday situations, such as budgeting. If you have a limit on how much you can spend (e.g., less than $40), and you've already spent $15, this inequality helps you determine how much more you can spend.
- Simplify the inequality to isolate $x$.
- The solution is $x < 40$.
- The correct option is $x<40$.
### Explanation
1. Understanding the Problem
We are asked to solve the inequality $x - 15 < 25$ for $x$. This means we want to find all values of $x$ that make the inequality true.
2. Isolating x
To isolate $x$, we need to get rid of the $-15$ on the left side of the inequality. We can do this by adding $15$ to both sides of the inequality:$$x - 15 + 15 < 25 + 15$$
3. Simplifying the Inequality
Now, we simplify both sides of the inequality:$$x < 40$$This means that any value of $x$ that is less than $40$ will satisfy the original inequality.
4. Finding the Correct Option
Comparing our solution $x < 40$ with the given options, we find that the correct answer is $x<40$.
### Examples
Understanding inequalities like this helps in everyday situations, such as budgeting. If you have a limit on how much you can spend (e.g., less than $40), and you've already spent $15, this inequality helps you determine how much more you can spend.
