1. solve the following inequality to find a range of values for x: -11 < -4-x < -7
2. solve the following inequality to find a range of values for x: -25 < -x < -10
-11 < 4-x < -7
-15 < -x < -11
15 > x > 11
or
11 < x < 15
similarly for the other
1. To solve the inequality -11 < -4 - x < -7, we'll start by simplifying it step by step.
First, let's deal with the first part of the inequality: -4 - x. Since we want to isolate x, we'll begin by subtracting 4 from both sides of the inequality:
-11 + 4 < -4 - x + 4 < -7 + 4.
This simplifies to:
-7 < -x < -3.
Now, we'll multiply both sides of the inequality by -1 to change the direction of the inequality signs:
-7 * -1 > -x * -1 > -3 * -1.
This gives us:
7 > x > 3.
Therefore, the range of values for x that satisfies the inequality is 3 < x < 7.
2. Now let's solve the inequality -25 < -x < -10.
Begin by multiplying both sides of the inequality by -1 to change the direction of the inequality signs:
-25 * -1 > -x * -1 > -10 * -1.
This yields:
25 > x > 10.
So, the range of values for x that satisfies the inequality is 10 < x < 25.