Alright, let's break this problem down step-by-step to find the solution:
1. Calculate the inner part inside the braces `{}`:
- Evaluate the division: [tex]\( \frac{4}{2} = 2 \)[/tex]
- Multiply the result by 72: [tex]\( 2 \times 72 = 144 \)[/tex]
- Divide by 36: [tex]\( \frac{144}{36} = 4 \)[/tex]
- Subtract 1: [tex]\( 4 - 1 = 1 \)[/tex]
So, the expression inside the braces evaluates to 1.
2. Calculate the part inside the brackets `[]`:
- Start with 3: [tex]\( 3 \)[/tex]
- Subtract the result from the braces: [tex]\( 3 - 1 = 2 \)[/tex]
So, the expression inside the brackets evaluates to 2.
3. Calculate the fraction inside the brackets:
- We have [tex]\(\frac{6}{7} \)[/tex] which needs to be multiplied by the result inside the brackets:
- [tex]\( \frac{6}{7} \times 2 = \frac{12}{7} \)[/tex]
So, the value inside the brackets becomes [tex]\( \frac{12}{7} \)[/tex].
4. Calculate the leftmost fraction:
- This is straightforward as given: [tex]\( \frac{3}{2} = 1.5 \)[/tex]
5. Final calculation by subtracting the two fractions:
- We need to find [tex]\( 1.5 - \frac{12}{7} \)[/tex]:
- [tex]\( \frac{12}{7} \approx 1.7142857142857142 \)[/tex]
- Subtract: [tex]\( 1.5 - 1.7142857142857142 = -0.2142857142857142 \)[/tex]
Therefore, the final answer to the expression is approximately [tex]\( -0.2142857142857142 \)[/tex].
