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Solve for b
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b+4=a\left(c+d\right)
Multiply both sides of the equation by c+d.
b+4=ac+ad
Use the distributive property to multiply a by c+d.
ac+ad=b+4
Swap sides so that all variable terms are on the left hand side.
\left(c+d\right)a=b+4
Combine all terms containing a.
\frac{\left(c+d\right)a}{c+d}=\frac{b+4}{c+d}
Divide both sides by c+d.
a=\frac{b+4}{c+d}
Dividing by c+d undoes the multiplication by c+d.