Are the inequalities x > 8 and -x < 8 equivalant? Why or why not?
x > 8 -X < 8.
-X < 8
Solve for x:
Multiply both side by -1 and reverse
inequality sign
X > -8
Now you can see by inspection that they
are not identical.
OOPS$! HENRY NOT ANON.
To determine if the inequalities x > 8 and -x < 8 are equivalent, we need to compare their solutions.
1. Let's start with x > 8:
- This inequality states that x is greater than 8.
- To find the solution, we need to consider all values of x that satisfy this inequality.
- One way to do this is by choosing a number larger than 8 and substituting it into the inequality to see if it holds.
- For example, if we choose x = 10, we have 10 > 8, which is true.
- This inequality holds true for any value of x greater than 8.
- Therefore, the solution to x > 8 is all values of x that are greater than 8.
2. Now let's consider -x < 8:
- This inequality states that the negative of x is less than 8.
- To find the solution, we can multiply both sides of the inequality by -1 (remembering to reverse the inequality sign) to get x > -8.
- This inequality states that x is greater than -8.
- Similar to the first inequality, we can choose a number larger than -8, like x = 0, and substitute it into the inequality to check its validity.
- We have 0 > -8, which is also true.
- Hence, the solution to -x < 8 (or x > -8) is all values of x that are greater than -8.
Comparing the solutions, we can see that the solution to x > 8 includes all values greater than 8, while the solution to x > -8 includes all values greater than -8. Therefore, the inequalities x > 8 and -x < 8 are NOT equivalent, as their solutions are different.