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Artemon [7]
3 years ago
7

Expanding and Adding Expressions Use the expansion shown to simplify the expression. One-half (3 x minus two-thirds y) + 3 (Star

tFraction x over 2 EndFraction + one-half y) Equals (one-half) (StartFraction 3 over 1 EndFraction x) + (one-half) (Negative two-thirds y) + (StartFraction 3 over 1 EndFraction) (one-half x) + (StartFraction 3 over 1 EndFraction) (one-half y) Equals (three-halves x) + (negative one-third y) + (three-halves x) + (three-halves y) = 3x + y
Mathematics
1 answer:
Lisa [10]3 years ago
6 0

Answer:

3x+\frac{7}{6}y

Step-by-step explanation:

To simplify the expression, we first open the parenthesis, then we collect all the like terms. Lastly we simplify the like terms to its simplest form. Given that:

\frac{1}{2}(3x-\frac{2}{3} y)+3(\frac{x}{2}+\frac{1}{2}y )\\\\Firstly, we\ expand\ the\ parenthesis:\\\\=\frac{1}{2}(3x)-\frac{1}{2}(\frac{2}{3} y)+3\frac{x}{2}+3(\frac{1}{2} y)\\

=\frac{3}{2}x-\frac{1}{3}y +\frac{3}{2}x+\frac{3}{2} y\\\\  Collecting\ like\ terms:\\\\=\frac{3}{2}x+\frac{3}{2}x-\frac{1}{3}y+\frac{3}{2}y\\\\Adding \ terms:\\\\=3x  +\frac{7}{6}y

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