explanation:
To determine the values that make the inequality -r ≤ 7 - r ≤ 7 true, we need to analyze the given options:
-12 -8 -7.1 -7 -6.9 -6 -2 0 2 6 6.9 7 7.1 8 12
To satisfy the first inequality, -r ≤ 7 - r, we need to consider the values that make the left side less than or equal to the right side. In this case, any value of r would satisfy this inequality because the term "-r" cancels out on both sides.
To satisfy the second inequality, 7 - r ≤ 7, we need to consider the values that make the left side less than or equal to the right side. From the given options, the values that satisfy this inequality are:
-12 -8 -7.1 -7 -6.9 -6 -2 0 2 6 6.9 7
Now, let's combine the two inequalities to write an equivalent inequality in terms of r:
-r ≤ 7 - r ≤ 7
By subtracting 7 from all sides of the inequality, we get:
-r - 7 ≤ - r ≤ 7 - 7
Simplifying further, we have:
-r - 7 ≤ - r ≤ 0
Therefore, the equivalent inequality in terms of r is:
-r - 7 ≤ - r ≤ 0
Please note that the value of r does not affect the validity of the inequality.
