Title: Opération Delta

Réordonner les liges, sachant que :

\(
  \left\lbrace
\begin {array}{lcll}
a \Delta b & = & ab + a + b  &   (1)\\
3 \Delta 5 & = & 2 \Delta x  & (2)\\
\end {array}
   \right.
\)

- \(
\begin{array}{rcl}
\textrm{Si} \quad a \Delta b  & =  &  ab + a + b   &    \qquad (1)      \\
\textrm{alors} \quad 3 \Delta 5 & = &  3 \times 5 + 3 + 5 &
\end{array}
\)
- \(
\begin{array}{lcll}
\textrm{et puisque} &  3 \times 5 + 3 + 5 &=  23, &\\
\textrm{alors}  &  3 \Delta 5 &= 23 &\quad  (3)
\end{array}
\)
- \(
\begin{array}{rcll}
\textrm{Si} \qquad a \Delta b  & =  &  ab + a + b &    \qquad (1)      \\
\textrm{alors} \quad 2 \Delta x  & =&   2 x + 2 +x &
\end{array}
\)
- \(
\begin{array}{lcll}
\textrm{et puisque} &\quad 2 x + 2 +x &= 3 x + 2, & \\
\textrm{alors}   &  2 \Delta x & = 3x + 2 &\qquad  (4)
\end{array}
\)
- \(
\begin{array}{llll}
\textrm{puisque}   &   3 \Delta 5         & =  2 \Delta x &\quad (2) \\
\textrm{que}        &  3 \Delta 5          & = 23           & \quad  (3) \\
\textrm{at que } &   2 \Delta x        & = 3x + 2      & \quad (4) \\
\end{array}
  \)
- alors \( \quad 3x +2 = 23 \)
- Conclusion \( x = 7 \)