Solve for z.
2/3 = 2 + 3/2 z – 1/2
z = =
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To solve for ( z ) in the equation:
[
frac{2}{3} = 2 + frac{3}{2} z – frac{1}{2}
]
First, simplify the right side of the equation:
1. Combine the constant terms ( 2 ) and ( -frac{1}{2} ):
[
2 – frac{1}{2} = frac{4}{2} – frac{1}{2} = frac{3}{2}
]
So the equation becomes:
[
frac{2}{3} = frac{3}{2} + frac{3}{2} z
]
2. Now, isolate the term with ( z ). Subtract ( frac{3}{2} ) from both sides:
[
frac{2}{3} – frac{3}{2} = frac{3}{2} z
]
3. To combine the fractions on the left, find a common denominator (which is 6):
[
frac{2}{3} = frac{4}{6}, quad frac{3}{2} = frac{9}{6}
]
So,
[
frac{4}{6} – frac{9}{6} = frac{-