Select the values that make the inequality minus, 4, k, is less than 84−4k<−84 true. Then write an equivalent inequality, in terms of k.
To make the inequality true, we need to find the values of k that satisfy both conditions:
1. -4, k < 84 - 4k
2. 84 - 4k < -84
Let's solve the first inequality:
-4, k < 84 - 4k
Adding 4k to both sides:
4k - 4, k < 84
Combining like terms:
5k < 88
Dividing both sides by 5 (and flipping the inequality since we are dividing by a negative):
k > 88/5
Therefore, the first part of the inequality is satisfied when k is greater than 88/5.
Now let's solve the second inequality:
84 - 4k < -84
Subtracting 84 from both sides:
-4k < -168
Dividing both sides by -4 (and flipping the inequality since we are dividing by a negative):
k > 42
Therefore, the second part of the inequality is satisfied when k is greater than 42.
To write an equivalent inequality in terms of k, we can combine the two parts:
k > 42 and k > 88/5
Since the second part is a stricter condition, we can simplify it to:
k > 88/5
Hence, the equivalent inequality in terms of k is k > 88/5.