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y-1=-\frac{3}{2}x-\frac{9}{2}
Use the distributive property to multiply -\frac{3}{2} by x+3.
-\frac{3}{2}x-\frac{9}{2}=y-1
Swap sides so that all variable terms are on the left hand side.
-\frac{3}{2}x=y-1+\frac{9}{2}
Add \frac{9}{2} to both sides.
-\frac{3}{2}x=y+\frac{7}{2}
Add -1 and \frac{9}{2} to get \frac{7}{2}.
\frac{-\frac{3}{2}x}{-\frac{3}{2}}=\frac{y+\frac{7}{2}}{-\frac{3}{2}}
Divide both sides of the equation by -\frac{3}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{y+\frac{7}{2}}{-\frac{3}{2}}
Dividing by -\frac{3}{2} undoes the multiplication by -\frac{3}{2}.
x=\frac{-2y-7}{3}
Divide y+\frac{7}{2} by -\frac{3}{2} by multiplying y+\frac{7}{2} by the reciprocal of -\frac{3}{2}.
y-1=-\frac{3}{2}x-\frac{9}{2}
Use the distributive property to multiply -\frac{3}{2} by x+3.
y=-\frac{3}{2}x-\frac{9}{2}+1
Add 1 to both sides.
y=-\frac{3}{2}x-\frac{7}{2}
Add -\frac{9}{2} and 1 to get -\frac{7}{2}.