To determine the values of [tex]\( k \)[/tex] that satisfy the inequality [tex]\(\frac{k-3}{4} > -2\)[/tex], we need to solve it step-by-step:
1. Begin with the given inequality:
[tex]\[
\frac{k-3}{4} > -2
\][/tex]
2. To clear the fraction, multiply both sides of the inequality by 4:
[tex]\[
k - 3 > -8
\][/tex]
3. Next, to isolate [tex]\( k \)[/tex], add 3 to both sides of the inequality:
[tex]\[
k > -5
\][/tex]
Now that we have the inequality [tex]\( k > -5 \)[/tex], we need to check which of the given options satisfy this condition.
- For [tex]\(k = -10\)[/tex]:
[tex]\[
-10 > -5 \quad \text{(False)}
\][/tex]
- For [tex]\(k = -7\)[/tex]:
[tex]\[
-7 > -5 \quad \text{(False)}
\][/tex]
- For [tex]\(k = -5\)[/tex]:
[tex]\[
-5 > -5 \quad \text{(False; it is equal, not greater)}
\][/tex]
- For [tex]\(k = -1\)[/tex]:
[tex]\[
-1 > -5 \quad \text{(True)}
\][/tex]
- For [tex]\(k = 0\)[/tex]:
[tex]\[
0 > -5 \quad \text{(True)}
\][/tex]
The values of [tex]\( k \)[/tex] that satisfy the inequality [tex]\(\frac{k-3}{4} > -2\)[/tex] are:
[tex]\[
k = -1 \quad \text{and} \quad k = 0
\][/tex]
