Final answer:
The values of 'a' and 'b' in the inequality 'a < 5x < b' are found by dividing the original inequality '15 < 5x < 30' by 5, yielding '3 < x < 6'. Multiplying these new bounds by 5 gives us 'a = 15' and 'b = 30'.
Step-by-step explanation:
To find the values of a and b given the inequality 15 < 5x < 30, we simply solve for x by dividing all parts of the inequality by 5.
So, dividing each part by 5, we get:
\(\frac{15}{5} < \frac{5x}{5} < \frac{30}{5}\)
\(3 < x < 6\)
Now, because the inequality involves 5x, we can develop a new inequality that represents the original question which is "a < 5x < b". Since we have found that "3 < x < 6", we need to find 5 times the lower and the upper limit of x to find a and b respectively.
So:
\(a = 5 \times 3 = 15\)
\(b = 5 \times 6 = 30\)
Thus, the values of a and b are 15 and 30, respectively. We can say that the inequality a < 5x < b becomes 15 < 5x < 30, which is the inequality we started with, confirming our answer.