Question

select the values that make the inequality $-k < 7$ true. then write an equivalent inequality, in terms of $k$. (numbers written in order from least to greatest going across.) answer attempt 1 out of 2 -12 -8 -7.1 -7 -6.9 -6 -2 0 2 6 6.9 7 7.1 8 12 equivalent inequality: $k$ $\square$ submit answer

Explanation:

Step1: Solve the inequality \(-k < 7\)

To solve for \(k\), we multiply both sides of the inequality by \(-1\). Remember that when we multiply or divide an inequality by a negative number, the direction of the inequality sign changes. So, multiplying both sides by \(-1\) gives:
\(k > -7\)

Step2: Identify values greater than \(-7\)

Now we check each value:

• \(-12\): \(-12 < -7\) (not valid)
• \(-8\): \(-8 < -7\) (not valid)
• \(-7.1\): \(-7.1 < -7\) (not valid)
• \(-7\): \(-7 = -7\) (not valid, since we need \(k > -7\))
• \(-6.9\): \(-6.9 > -7\) (valid)
• \(-6\): \(-6 > -7\) (valid)
• \(-2\): \(-2 > -7\) (valid)
• \(0\): \(0 > -7\) (valid)
• \(2\): \(2 > -7\) (valid)
• \(6\): \(6 > -7\) (valid)
• \(6.9\): \(6.9 > -7\) (valid)
• \(7\): \(7 > -7\) (valid)
• \(7.1\): \(7.1 > -7\) (valid)
• \(8\): \(8 > -7\) (valid)
• \(12\): \(12 > -7\) (valid)

Answer:

Valid values: \(-6.9\), \(-6\), \(-2\), \(0\), \(2\), \(6\), \(6.9\), \(7\), \(7.1\), \(8\), \(12\)
Equivalent Inequality: \(k > -7\)