Solve each inequality x+8>18
The Correct Answer and Explanation is:
To solve the inequality ( x + 8 > 18 ), we can follow these steps:
Step 1: Isolate the variable ( x )
The goal is to solve for ( x ), so we need to isolate ( x ) on one side of the inequality.
Start with the original inequality:
[
x + 8 > 18
]
To isolate ( x ), subtract 8 from both sides of the inequality:
[
x + 8 – 8 > 18 – 8
]
Simplifying both sides:
[
x > 10
]
Step 2: Interpret the solution
The solution to the inequality is ( x > 10 ). This means that ( x ) can be any value greater than 10, but not equal to 10.
In other words, the solution is the set of all real numbers greater than 10, expressed in interval notation as:
[
(10, \infty)
]
This interval notation represents all numbers starting just after 10 and extending infinitely to the right.
Step 3: Verify the solution
To verify, choose a value for ( x ) that is greater than 10 and substitute it back into the original inequality.
For example, let’s choose ( x = 11 ):
[
x + 8 = 11 + 8 = 19
]
Since 19 is greater than 18, the inequality holds true, confirming that the solution is correct.
Now, let’s test with a value less than 10, say ( x = 9 ):
[
x + 8 = 9 + 8 = 17
]
Since 17 is not greater than 18, the inequality is not satisfied for ( x = 9 ), which further confirms that ( x > 10 ) is the correct solution.
Conclusion
Thus, the solution to the inequality ( x + 8 > 18 ) is ( x > 10 ), which can be written in interval notation as ( (10, \infty) ).