Final answer:
To find the possible range of values for 8 - 20ax given the inequality 5ax - 2 < 7, we first solve for x, leading to x < 9 / (5a). Substituting this into 8 - 20ax gives us a possible value of less than -28.
Step-by-step explanation:
The original inequality provided in the question seems to have some typographical errors, but we can interpret the core question to be about finding the possible range of values of 8 - 20ax given that 5 - 2 < 7 5ax - 2 < 7 when a is a positive constant. Assuming the inequality should be 5ax - 2 < 7, we can solve for x as follows:
- Add 2 to both sides: 5ax < 9
- Divide by 5a (since a is positive, the inequality sign remains the same): x < 9 / (5a)
Now we can substitute this into 8 - 20ax and find the possible range for this expression:
- Substitute x < 9 / (5a) into the expression: 8 - 20a(9 / (5a))
- Simplify the expression: 8 - 36
This means that the possible range of values for 8 - 20ax is less than -28.
To find the possible range of values of 8 − 20ax-20, we first look at the given inequality 5ax-2 < 7. Since a is a positive constant, we can rearrange the inequality to isolate ax:
ax < 9.
Since a is positive, dividing both sides by a does not change the direction of the inequality, so we have x < 9/a.
Now we substitute this into the expression 8 − 20ax-20 to get:
8 − 20(9/a) = 8 - 180/a.
Since a is positive, the value of 8 - 180/a is decreasing as a increases. Therefore, the possible range of values of 8 − 20ax-20 is (-∞, 8 - 180/a].