Question

Solve for \(x\) in \(\frac{3 x-2}{2}=x+1\)

Answer 1

(1) Simplify \(\frac{3 x-2}{2}\) to \(-1+\frac{3 x}{2}\).
\[
-1+\frac{3 x}{2}=x+1
\]
(2) Regroup terms.
\[
\frac{3 x}{2}-1=x+1
\]
(3) Multiply both sides by 2 .
\[
3 x-2=2 x+2
\]
(4) Add 2 to both sides.
\[
3 x=2 x+2+2
\]
(5) Simplify \(2 x+2+2\) to \(2 x+4\).
\[
3 x=2 x+4
\]
(6) Subtract \(2 x\) from both sides.
\[
3 x-2 x=4
\]
(7) Simplify \(3 x-2 x\) to \(x\).
\[
x=4
\]