We find the missing number as follows:
[tex]2(4x-12)=2(-3x-10)+\mleft\lbrace \mright\rbrace x+10\Rightarrow8x-24=-6x-20+\mleft\lbrace \mright\rbrace x+10[/tex][tex]\Rightarrow8x+6x-\mleft\lbrace \mright\rbrace x=-20+10+24\Rightarrow14x-\mleft\lbrace \mright\rbrace x=14[/tex][tex]\Rightarrow x(14-\mleft\lbrace \mright\rbrace)=14[/tex][tex]14-\mleft\lbrace \mright\rbrace=0\Rightarrow\mleft\lbrace \mright\rbrace=14[/tex]
If we have that "blank" has a value of 14, then the equation would not make sense and therefore has no solutions.
