Final answer:
To solve the equation 2(3 - x) + 5 < 392(x - 3) + 5 > 39, distribute the terms inside the parentheses and simplify each side separately. Then, isolate x by subtracting and dividing to find the range of values that satisfy the inequality. The solution for x is 3 < x < 3.0014.
Step-by-step explanation:
To solve the equation 2(3 - x) + 5 < 392(x - 3) + 5 > 39, we need to simplify each side of the inequality separately. On the left side, distribute the 2 to both terms inside the parentheses. This gives us 6 - 2x + 5. Simplifying further, we have 11 - 2x. On the right side, distribute the 392 to both terms inside the parentheses. This gives us 392x - 1176 + 5. Simplifying further, we have 392x - 1171. Now, we have the inequality 11 - 2x < 392x - 1171 < 39. We can solve this inequality by isolating x and finding the values of x that satisfy the inequality.
To isolate x, we first subtract 11 from all parts of the inequality. This gives us -2x < 392x - 1182 < 28. Next, we can combine like terms by subtracting 392x from all parts of the inequality. This gives us -394x < -1182 < 28. Finally, we divide all parts of the inequality by -394, remembering to reverse the direction of the inequality symbols because we are dividing by a negative number. This gives us x > 3 and x < 3.0014. Therefore, the solution for x is 3 < x < 3.0014.