Select the values that make the inequality minus, 8, h, is less than, 24−8h<24 true. Then write an equivalent inequality, in terms of hh.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 3
-13 -8 -6
-4 -3 -2
0 2 7
To solve the inequality -8h < 24 - 8h < 24, we can start by combining like terms:
-8h < 24 - 8h < 24
Next, let's isolate the variable h by adding 8h to both sides:
0 < 24 < 8h + 8h
Simplifying further, we have:
0 < 24 < 16h
To solve for h, divide both sides of the inequality by 16:
0/16 < 24/16 < 16h/16
0 < 3/2 < h
So, the inequality 0 < 3/2 < h represents the same solution as -8h < 24 - 8h < 24.
Now, let's select the values that make the inequality true in order to write an equivalent inequality in terms of h. Looking at the options you provided:
-13 -8 -6
-4 -3 -2
0 2 7
We can choose any value for h as long as it satisfies the inequality 0 < 3/2 < h. From the options given, the values of h that make the inequality true are:
-2, -3, -4, -6, -8, -13
So, the equivalent inequality in terms of h, using the selected values, would be:
-13 < h < -2