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

[mathdad]

|[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

 

[kaliprasad]

|[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

 

[MarkFL]

|[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

 

[mathdad]

Thank you. I can take it from here.