Solve for b. 1/4 + 1 = -1/2b + 3 b =

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: