To determine which values satisfy the inequality [tex]\(\frac{k-3}{4} > -2\)[/tex], we will solve the inequality step-by-step and then check which of the given values satisfy the solution.
1. Start with the inequality:
[tex]\[\frac{k-3}{4} > -2\][/tex]
2. Clear the fraction by multiplying both sides by 4:
[tex]\[k - 3 > -2 \times 4\][/tex]
[tex]\[k - 3 > -8\][/tex]
3. Isolate [tex]\(k\)[/tex] by adding 3 to both sides:
[tex]\[k > -8 + 3\][/tex]
[tex]\[k > -5\][/tex]
Now we have the solution to the inequality: [tex]\(k > -5\)[/tex].
4. Determine which of the given values satisfy [tex]\(k > -5\)[/tex]:
- [tex]\(k = -10\)[/tex]: [tex]\(-10 > -5\)[/tex] (False)
- [tex]\(k = -7\)[/tex]: [tex]\(-7 > -5\)[/tex] (False)
- [tex]\(k = -5\)[/tex]: [tex]\(-5 > -5\)[/tex] (False)
- [tex]\(k = -1\)[/tex]: [tex]\(-1 > -5\)[/tex] (True)
- [tex]\(k = 0\)[/tex]: [tex]\(0 > -5\)[/tex] (True)
Therefore, the values [tex]\(-1\)[/tex] and [tex]\(0\)[/tex] satisfy the inequality [tex]\(\frac{k-3}{4} > -2\)[/tex].
The two options that are solutions to the inequality are:
- [tex]\(k = -1\)[/tex]
- [tex]\(k = 0\)[/tex]
