#### Answer

\[x=\frac{4}{3}\]

#### Work Step by Step

The equation is\[-2\left\{ 7-\left[ 4-2\left( 1-x \right)+3 \right] \right\}=10-\left[ 4x-2\left( x-3 \right) \right]\].
Use the order of operations,
\[\begin{align}
& -2\left\{ 7-\left[ 4-2\left( 1-x \right)+3 \right] \right\}=10-\left[ 4x-2\left( x-3 \right) \right] \\
& -2\left\{ 7-\left[ 4-2+2x+3 \right] \right\}=10-\left[ 4x-2x+6 \right] \\
& -2\left\{ 7-\left[ 5+2x \right] \right\}=10-\left[ 2x+6 \right] \\
& -2\left\{ 7-5-2x \right\}=10-2x-6
\end{align}\]
Further simplification,
\[\begin{align}
& -2\left\{ 2-2x \right\}=4-2x \\
& -4+4x=4-2x
\end{align}\]
Add\[2x\]to both sides of the equal sign,
\[\begin{align}
& -4+4x+2x=4-2x+2x \\
& -4+6x=4
\end{align}\]
Add \[4\]to both sides of the equal sign,
\[\begin{align}
& -4+6x+4=4+4 \\
& 6x=8 \\
& x=\frac{8}{6} \\
& x=\frac{4}{3}
\end{align}\]
Therefore, the value of \[x=\frac{4}{3}\]