Answer
The solution set of equation $7\left( x-2 \right)=4\left( x+1 \right)-21$ is $\left\{ -\left. 1 \right\} \right.$.
Work Step by Step
Consider the equation: $7\left( x-2 \right)=4\left( x+1 \right)-21$
The above equation can be written as:
$\begin{align}
& 7\left( x-2 \right)=4\left( x+1 \right)-21 \\
& 7x-14=4x+4-21 \\
\end{align}$
Take the terms containing x on the left hand side and constant terms on the right side
$\begin{align}
& 7x-4x=14+4-21 \\
& 3x=-3
\end{align}$
Divide both sides by $3$
$\begin{align}
& \frac{3x}{3}=\frac{-3}{3} \\
& x=-1
\end{align}$
Check:
For $x=-1$
Put $x=-1$ in $7\left( x-2 \right)=4\left( x+1 \right)-21$
$\begin{align}
& 7\left( x-2 \right)\overset{?}{\mathop{=}}\,4\left( x+1 \right)-21 \\
& 7\left( -1-2 \right)\overset{?}{\mathop{=}}\,4\left( -1+1 \right)-21 \\
& 7\left( -3 \right)\overset{?}{\mathop{=}}\,4\left( 0 \right)-21 \\
& -21=-21 \\
\end{align}$
Which is true.
Therefore, the solution set of the equation $7\left( x-2 \right)=4\left( x+1 \right)-21$ is $\left\{ -\left. 1 \right\} \right.$.
