Which expression is equivalent to ( (1/2)x – 2) (x + 3/4) ?

To find the equivalent expression to ( ((1/2)x – 2)(x + 3/4) ), we’ll use the distributive property (also known as the FOIL method for binomials).

Step 1: Distribute ( (1/2)x )

– ( (1/2)x cdot x = (1/2)x^2 )

– ( (1/2)x cdot (3/4) = frac{3}{8}x )

Step 2: Distribute (-2)

– ( -2 cdot x = -2x )

– ( -2 cdot (3/4) = -frac{3}{2} )

Step 3: Combine like terms

Combining all the terms we have:

[

(1/2)x^2 + frac{3}{8}x – 2x – frac{3}{2}

]

First, convert (-2x) to a fraction:

(-2x = -frac{16}{8}x)

Now we can combine the (x) terms:

[

frac{3}{8}x – frac{16}{8}x = -frac{13}{8}x

]

So, putting it all together, we have:

[

(1