Answer
The solution set is \[\varnothing \](the empty set).
Work Step by Step
The equation is\[2\left( 5x+58 \right)=10x+4\left( 21\div 3.5-11 \right)\].
Use the order of operations,
Work inside parentheses first,
\[\begin{align}
& 2\left( 5x+58 \right)=10x+4\left( 21\div 3.5-11 \right) \\
& 10x+116=10x+4\left( 6-11 \right) \\
& 10x+116=10x+4\left( -5 \right) \\
& 10x+116=10x-20
\end{align}\]
Subtract\[10x\] to both sides of the equal sign,
\[\begin{align}
& 10x+116-10x=10x-20-10x \\
& 116=-20
\end{align}\]
Therefore, the equation \[2\left( 5x+58 \right)=10x+4\left( 21\div 3.5-11 \right)\]is equivalent to the statement \[116=-20\].
Which is false for every value of \[x\].
Thus, the equation has no solution. The solution set is \[\varnothing \](the empty set).
