equations

3(x-4)=5 - (2x +3) has the solution x= 2 + 4/5 

change on term or sign to make the solution x=3

1.

\(\begin{array}{rcll} x &=& 2+ \frac45 \\ x +\frac15 &=& 2+ \frac45 +\frac15 \\ x +\frac15 &=& 3 \\\\ \bar{x} &=& x +\frac15 \qquad \text{ or } \qquad \\ \mathbf{x} &\mathbf{=}& \mathbf{\bar{x} - \frac15} \end{array}\)

2.

\(\begin{array}{rcll} 3(x-4) &=& 5 - (2x +3) \qquad & | \qquad \mathbf{x} = \mathbf{\bar{x} - \frac15} \\ 3(\mathbf{\bar{x} - \frac15}-4) &=& 5 - [2(\mathbf{\bar{x} - \frac15}) +3] \\ 3(\bar{x} - 4) -\frac35 &=& 5 - (2\bar{x}- \frac25 +3 ) \\ 3(\bar{x} - 4) -\frac35 &=& 5 - (2\bar{x} +3) + \frac25 \\ 3(\bar{x} - 4) &=& 5 - (2\bar{x} +3) + \frac25 +\frac35 \\ 3(\bar{x} - 4) &=& 5 - (2\bar{x} +3) + 1 \\ 3(\bar{x} - 4) &=& 6 - (2\bar{x} +3) \\\\ \mathbf{3( x - 4) } &\mathbf{=}& \mathbf{6 - (2x +3) \qquad \Rightarrow \qquad x=3 } \end{array}\)