Question

Which values are solutions to StartFraction k minus 3 Over 4 EndFraction >–2? Select two options.

k = –10
k = –7
k = –5
k = –1
k = 0

Answer 1

To solve the inequality \(\frac{k - 3}{4} > -2\), we first isolate \(k\).

1. Multiply both sides by 4 (since we are multiplying by a positive number, the inequality remains the same):
\[
k - 3 > -8
\]

2. Add 3 to both sides:
\[
k > -5
\]

Now we need to find the values from the provided options that satisfy \(k > -5\):

1. **k = -10**: \(-10 > -5\) is false.
2. **k = -7**: \(-7 > -5\) is false.
3. **k = -5**: \(-5 > -5\) is false (not strictly greater).
4. **k = -1**: \(-1 > -5\) is true.
5. **k = 0**: \(0 > -5\) is true.

The values that satisfy the inequality are \(k = -1\) and \(k = 0\).

**Thus, the two options are**:
- \(k = -1\)
- \(k = 0\)