State functions defining different intervals of a main function

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I have the function $f(x) = 4|3x-1|+|6x+3|$

I am supposed to state the partial functions without the absolute value notation for the different intervals.

I know that for:

$$x\ge 1/3, f(x) = 18x-1$$ $$x < -1/2, f(x) = -18x+1$$

I reached this conclusion from calculating assuming $x<0, x \le 0$ and then adjusting for the coefficients for $x$.

However I am not sure how to calculate the function for the interval $-1/2 \le x < 1/3$

Thanks in advance!