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

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Which expression is equivalent to ( (1/2)x – 2) (x + 3/4) ?
1/2 x² – 13/8 x + 3/2
1/2 x² – 13/8 x – 3/2
-9/8 x – 3/2
3/2 x – 5/4




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    1 Answer

    1. Quizzma Team

      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

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