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

To simplify this expression, let's first deal with the subtraction inside the parentheses and then distribute the negative sign to each term inside the parentheses. We'll combine like terms after that.

The expression given is:

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

First, let's convert the mixed numbers to improper fractions to make calculations easier.

• 4 7/32 is already an improper fraction.
• 3 3/4 can be converted as follows: (3 × 4 + 3)/4 = (12 + 3)/4 = 15/4
• 1 7/32 is already an improper fraction.

Now the expression becomes:

(4 7/32)x - ((15/4)x - (1 7/32)x)

Now we subtract the second part of the parentheses:

[(4 7/32) - (15/4) + (1 7/32)]x

Since (4 7/32) and (1 7/32) are like terms, we add them together:

(4 7/32 + 1 7/32) - (15/4)

To add these two fractions, we simply add their numerators because they have the same denominator:

(4 + 1) + (7/32 + 7/32) = 5 + (14/32)

Now we must simplify the fraction 14/32 by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

14 ÷ 2 = 7 32 ÷ 2 = 16

So, 14/32 simplifies to 7/16, and the expression now is:

(5 + 7/16) - (15/4)x

Next, let's simplify the (15/4)x term. We need a common denominator to combine (5 + 7/16) and (15/4). The lowest common denominator for 16 and 4 is 16. So, we convert (15/4) to a fraction with a denominator of 16:

(15/4) × (4/4) = (15 × 4)/(4 × 4) = 60/16

Now we can subtract (60/16)x from (5 + 7/16):

5 + 7/16 - 60/16

We convert 5 to a fraction with a denominator of 16:

5 × (16/16) = 80/16

So the expression now is:

(80/16) + 7/16 - 60/16

Now, let's combine the terms:

(80 + 7 - 60)/16

Which simplifies to:

27/16

The final simplified expression is:

(27/16)x

Here we have an expression with a single term in x, where the coefficient of x is the improper fraction 27/16.