Final answer:
To solve the inequality 4 < 2(1-3x) < 10, we divide by 2, subtract 1, and divide by -3 while reversing inequality signs. The solution is -4/3 < x < -1/3, where x lies between but does not include these two values.
Step-by-step explanation:
To solve the inequality 4 < 2(1-3x) < 10, we need to isolate the variable x. First, let's divide the entire inequality by 2 to simplify it:
2 < 1 - 3x < 5
Next, we subtract 1 from all three parts of the inequality:
1 < -3x < 4
Now we divide by -3, remembering to reverse the inequality symbols because we are dividing by a negative number:
-\(\frac{1}{3}\) > x > -\(\frac{4}{3}\)
To write the solution in the correct order, we write the smallest number on the left, giving us the final solution:
x < -\(\frac{1}{3}\)
x > -\(\frac{4}{3}\)
This means x is between -\(\frac{4}{3}\) and -\(\frac{1}{3}\), but not including -\(\frac{1}{3}\) and -\(\frac{4}{3}\).