Question

Find the missing number so that the equation has no solutions. 2(4x - 12) = 2(-3x - 10) + X + 10

Answer 1

We find the missing number as follows:

`2(4x-12)=2(-3x-10)+\mleft\lbrace \mright\rbrace x+10\Rightarrow8x-24=-6x-20+\mleft\lbrace \mright\rbrace x+10`
`\Rightarrow8x+6x-\mleft\lbrace \mright\rbrace x=-20+10+24\Rightarrow14x-\mleft\lbrace \mright\rbrace x=14`
`\Rightarrow x(14-\mleft\lbrace \mright\rbrace)=14`
`14-\mleft\lbrace \mright\rbrace=0\Rightarrow\mleft\lbrace \mright\rbrace=14`

If we have that "blank" has a value of 14, then the equation would not make sense and therefore has no solutions.