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

Find the missing number so that the equation has no solutions. 2(4x - 12) = 2(-3x-example-1

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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.

User TimDog
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