I'm looking a problem in my textbook and I don't understand how it goes from one step to another.
It starts out as:
(120 * 2^5)/(180 * n^4) < 1/10^4
That turns into:
n^4 > (64 * 10^4)/3
Can you please explain the steps between those two?
Thanks
Of course! Let's break down the steps between the two expressions:
Step 1: Start with the inequality expression:
(120 * 2^5)/(180 * n^4) < 1/10^4
Step 2: Simplify the numerator and denominator by applying the exponent 5 to 2:
(120 * 32)/(180 * n^4) < 1/10^4
Step 3: Multiply the numerator:
3840/(180 * n^4) < 1/10^4
Step 4: Simplify the denominator by multiplying the exponents of 10:
3840/(180 * n^4) < 1/10000
Step 5: Multiply the numerator and denominator by 10000 (to remove the decimals):
(10000 * 3840)/(180 * n^4) < 1
Step 6: Simplify the expression in the numerator:
38400000/(180 * n^4) < 1
Step 7: Simplify the denominator:
213333.33 / (n^4) < 1
Step 8: Multiply both sides of the inequality by n^4 to eliminate the fraction:
213333.33 < n^4
Step 9: Rearrange the inequality:
n^4 > 213333.33
Step 10: Simplify the fraction on the right-hand side:
n^4 > (6400000/3)
And there you have it! The expression (120 * 2^5)/(180 * n^4) < 1/10^4 simplifies to n^4 > (6400000/3), which is written as n^4 > (64 * 10^4)/3.