MHB Can I use the theorem for solving the given inequality?

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The discussion focuses on using a theorem to solve the inequality |[3(x - 2)/4] + 4(x - 1)/3| ≤ 2. The theorem states that if a > 0, then |u| < a is equivalent to -a < u < a. Participants confirm that this theorem can be applied to the given inequality. By multiplying through by 12, the inequality simplifies to |25x - 34| ≤ 24. The final solution indicates that the values of x are within 24/25 units from 34/25 on the number line.
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|[3(x - 2)/4] + 4(x - 1)/3| ≤ 2

Can I use the following theorem?

If a > 0, then | u | < a if and only if -a < u < a
 
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RTCNTC said:
|[3(x - 2)/4] + 4(x - 1)/3| ≤ 2

Can I use the following theorem?

If a > 0, then | u | < a if and only if -a < u < a

yes
 
RTCNTC said:
|[3(x - 2)/4] + 4(x - 1)/3| ≤ 2

Can I use the following theorem?

If a > 0, then | u | < a if and only if -a < u < a

I'd begin by multiplying through by 12 to get:

$$\left|9(x-2)+16(x-1)\right|\le24$$

$$|25x-34|\le24$$

$$\left|x-\frac{34}{25}\right|\le\frac{24}{25}$$

Now it's obvious the solution is the set of all real numbers whose distance on the number line from 34/25 is less than or equal to 24/25...:D
 
Thank you. I can take it from here.
 
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