Answer :
To solve the inequality \(-s \leq -7\) and express it in terms of \(s\), we need to isolate \(s\). Here's a detailed, step-by-step solution:
1. Given inequality: \(-s \leq -7\).
2. To isolate \(s\), divide both sides of the inequality by \(-1\). Remember, dividing or multiplying an inequality by a negative number reverses the inequality sign:
[tex]\[ -s \leq -7 \implies s \geq 7 \][/tex]
So, the equivalent inequality in terms of \(s\) is \(s \geq 7\).
3. Now, we need to determine which values from the given set satisfy the inequality \(s \geq 7\). The values given are:
[tex]\[ -12, -8, -7, -6.9, -2, 0, 6, 6.9, 7.1, 8 \][/tex]
4. We compare each value to 7:
- \(-12 < 7\) (does not satisfy \(s \geq 7\))
- \(-8 < 7\) (does not satisfy \(s \geq 7\))
- \(-7 < 7\) (does not satisfy \(s \geq 7\))
- \(-6.9 < 7\) (does not satisfy \(s \geq 7\))
- \(-2 < 7\) (does not satisfy \(s \geq 7\))
- \(0 < 7\) (does not satisfy \(s \geq 7\))
- \(6 < 7\) (does not satisfy \(s \geq 7\))
- \(6.9 < 7\) (does not satisfy \(s \geq 7\))
- \(7.1 > 7\) (satisfies \(s \geq 7\))
- \(8 > 7\) (satisfies \(s \geq 7\))
5. The values that make the inequality \(s \geq 7\) true are \(7.1\) and \(8\).
Therefore, the values from the given set that satisfy the inequality \(-s \leq -7\) are:
[tex]\[ 7.1, 8 \][/tex]
And the equivalent inequality in terms of \(s\) is:
[tex]\[ s \geq 7 \][/tex]
1. Given inequality: \(-s \leq -7\).
2. To isolate \(s\), divide both sides of the inequality by \(-1\). Remember, dividing or multiplying an inequality by a negative number reverses the inequality sign:
[tex]\[ -s \leq -7 \implies s \geq 7 \][/tex]
So, the equivalent inequality in terms of \(s\) is \(s \geq 7\).
3. Now, we need to determine which values from the given set satisfy the inequality \(s \geq 7\). The values given are:
[tex]\[ -12, -8, -7, -6.9, -2, 0, 6, 6.9, 7.1, 8 \][/tex]
4. We compare each value to 7:
- \(-12 < 7\) (does not satisfy \(s \geq 7\))
- \(-8 < 7\) (does not satisfy \(s \geq 7\))
- \(-7 < 7\) (does not satisfy \(s \geq 7\))
- \(-6.9 < 7\) (does not satisfy \(s \geq 7\))
- \(-2 < 7\) (does not satisfy \(s \geq 7\))
- \(0 < 7\) (does not satisfy \(s \geq 7\))
- \(6 < 7\) (does not satisfy \(s \geq 7\))
- \(6.9 < 7\) (does not satisfy \(s \geq 7\))
- \(7.1 > 7\) (satisfies \(s \geq 7\))
- \(8 > 7\) (satisfies \(s \geq 7\))
5. The values that make the inequality \(s \geq 7\) true are \(7.1\) and \(8\).
Therefore, the values from the given set that satisfy the inequality \(-s \leq -7\) are:
[tex]\[ 7.1, 8 \][/tex]
And the equivalent inequality in terms of \(s\) is:
[tex]\[ s \geq 7 \][/tex]
