Six less than the product of four and a number is less than 0.5 times the opposite of the number
My answer
6-4n< 0.5/n
Nope. try
4n-6 < 0.5(-n)
"opposite" is a vague term. Usually it means negative. You have interpreted it as reciprocal.
In either case,
"the product of four and a number" is 4n
six less than that is 4n-6, not 6-4n.
To solve this inequality, let's break it down step by step:
1. "The product of four and a number" can be written as 4n.
2. "Six less than the product of four and a number" is then 4n - 6.
3. "The opposite of the number" is -n.
4. "0.5 times the opposite of the number" is 0.5 * (-n), which can be written as -0.5n.
Now, we have the inequality:
4n - 6 < -0.5n
To solve for n, we can combine like terms by adding 0.5n to both sides of the inequality:
4n + 0.5n - 6 < 0
Simplifying the left side of the inequality gives us:
4.5n - 6 < 0
Next, we can add 6 to both sides of the inequality:
4.5n < 6
Finally, to solve for n, divide both sides of the inequality by 4.5:
n < 6/4.5
The final solution is:
n < 1.33