Solve for b.
1/4 + 1 = -1/2b + 3
b =
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To solve for ( b ) in the equation:
[
frac{1}{4} + 1 = -frac{1}{2}b + 3
]
First, simplify the left side:
[
frac{1}{4} + 1 = frac{1}{4} + frac{4}{4} = frac{5}{4}
]
Now, the equation becomes:
[
frac{5}{4} = -frac{1}{2}b + 3
]
Next, subtract 3 from both sides. To do this, express 3 with a denominator of 4:
[
3 = frac{12}{4}
]
So:
[
frac{5}{4} – frac{12}{4} = -frac{1}{2}b
]
This simplifies to:
[
-frac{7}{4} = -frac{1}{2}b
]
Now, multiply both sides by -1 to eliminate the negative sign:
[
frac{7}{4} = frac{1}{2}b
]
Next, to isolate ( b ), multiply both sides by 2:
[
b = 2 cdot frac{7}{4} = frac{14}{4} = frac{7}{2}
]
Thus, the solution is: