4 7/32x-(3 3/4x - 1 7/32x)

To solve the expression, we need to simplify it by applying the distributive property and combining like terms. Let's break it down step by step:

1. Convert the mixed numbers to improper fractions to make them easier to work with.

For 4 7/32, the improper fraction is (4 × 32) + 7 over 32, which is 135/32. For 3 3/4, the improper fraction is (3 × 4) + 3 over 4, which is 15/4. To work with 32 as a common denominator, we have to convert 15/4 into an equivalent fraction with a denominator of 32. This means we multiply both the numerator and denominator by 8: (15 × 8) / (4 × 8) = 120/32. For 1 7/32, the improper fraction is (1 × 32) + 7 over 32, which is 39/32.

2. Replace the mixed numbers with their respective improper fractions:

(135/32)x - ( (120/32)x - (39/32)x )

3. Distribute the negative sign inside the parentheses:

(135/32)x - (120/32)x + (39/32)x

4. Combine like terms by adding or subtracting the coefficients (the numerators of the fractions before the x's):

(135/32)x - (120/32)x + (39/32)x = (135 - 120 + 39)/32 x = (15 + 39)/32 x = 54/32 x

5. Simplify the fraction if possible. Both 54 and 32 have a common factor of 2:

54/32 = (54 ÷ 2) / (32 ÷ 2) = 27/16

So, the simplified expression would be:

27/16 x

This is your final simplified expression.