Determine whether each of the integers from-5 to 5 are is a solution of the inequality I x-5 I+3>5.
|x-5| > 2 ???
-5 ---> 10 yes
.
.
-3 ----> 8 yes
0 ---> 5 yes
2 ---> 3 yes
3 ---> 2 no
4----> 1 no
5----> 0 no
To determine whether each of the integers from -5 to 5 are solutions of the inequality |x - 5| + 3 > 5, we need to substitute each integer into the inequality and check if the inequality holds true.
1. Let's first consider x = -5:
|(-5) - 5| + 3 > 5
|-10| + 3 > 5
10 + 3 > 5
13 > 5
Since 13 is greater than 5, this inequality holds true for x = -5.
2. Now, let's consider x = -4:
|(-4) - 5| + 3 > 5
|-9| + 3 > 5
9 + 3 > 5
12 > 5
Since 12 is greater than 5, this inequality holds true for x = -4.
3. Moving on to x = -3:
|(-3) - 5| + 3 > 5
|-8| + 3 > 5
8 + 3 > 5
11 > 5
Since 11 is greater than 5, this inequality holds true for x = -3.
4. Now, x = -2:
|(-2) - 5| + 3 > 5
|-7| + 3 > 5
7 + 3 > 5
10 > 5
Again, the inequality holds true for x = -2.
5. Next, x = -1:
|(-1) - 5| + 3 > 5
|-6| + 3 > 5
6 + 3 > 5
9 > 5
Once again, the inequality holds true for x = -1.
6. Moving on, x = 0:
|(0) - 5| + 3 > 5
|-5| + 3 > 5
5 + 3 > 5
8 > 5
The inequality is true for x = 0.
7. Now, x = 1:
|(1) - 5| + 3 > 5
|-4| + 3 > 5
4 + 3 > 5
7 > 5
The inequality holds true for x = 1.
8. Next, x = 2:
|(2) - 5| + 3 > 5
|-3| + 3 > 5
3 + 3 > 5
6 > 5
The inequality is true for x = 2.
9. Now, x = 3:
|(3) - 5| + 3 > 5
|-2| + 3 > 5
2 + 3 > 5
5 > 5
Since 5 is not greater than 5, this inequality does not hold true for x = 3.
10. Finally, x = 4:
|(4) - 5| + 3 > 5
|-1| + 3 > 5
1 + 3 > 5
4 > 5
Similarly, the inequality doesn't hold true for x = 4.
11. Lastly, x = 5:
|(5) - 5| + 3 > 5
|0| + 3 > 5
0 + 3 > 5
3 > 5
The inequality also doesn't hold true for x = 5.
To summarize, the integers from -5 to 5 that are solutions of the inequality |x - 5| + 3 > 5 are: -5, -4, -3, -2, -1, 0, 1, and 2.
To determine whether each integer from -5 to 5 is a solution of the inequality |x - 5| + 3 > 5, we can substitute each integer into the inequality and check if the statement holds true or false.
Let's start by substituting -5 into the inequality:
|x - 5| + 3 > 5 becomes |-5 - 5| + 3 > 5 which simplifies to |-10| + 3 > 5.
|-10| is equal to 10, so the inequality becomes 10 + 3 > 5, which simplifies to 13 > 5. This is true, so -5 is a solution to the inequality.
Now let's substitute -4:
|x - 5| + 3 > 5 becomes |-4 - 5| + 3 > 5 which simplifies to |-9| + 3 > 5.
|-9| is equal to 9, so the inequality becomes 9 + 3 > 5, which simplifies to 12 > 5. This is true, so -4 is a solution to the inequality.
We can follow this process for all the remaining integers from -3 to 5. By substituting each integer into the inequality and checking if the statement holds true or false, we can determine whether the integers from -5 to 5 are solutions to the inequality.