Question

match each equaton on the left with its solution on the right. No answer on the right will be used twice. 2x + 3(x - 2) = 6( x + 1) +x2x + 3(x - 2) = 6( x - 1) - x2x + 3(x - 2) = 6( x - 1) + x2x + 3 (x - 1) = 6( x -1) - xx=0no solution x= -6all real numbers

Answer 1

The expressions 2x + 3(x - 2) = 6( x + 1) +x can be solved as

`\begin{gathered} 2x+3\mleft(x-2\mright)=6(x+1)+x \\ 2x+3x-6=6x+6+x \\ 5x-6=6x+6+x \\ -6-6=6x+x-5x \\ -12=2x \\ x=-6 \end{gathered}`

Hence, for 2x + 3(x - 2) = 6( x + 1) +x, x=-6.

The expression 2x + 3(x - 2) = 6( x - 1) - x can be solved as

`\begin{gathered} 2x+3\mleft(x-2\mright)=6(x-1)-x \\ 2x+3x-6=6x-6-x \\ 5x-6=5x-6 \\ 0=0 \end{gathered}`

So, expression 2x + 3(x - 2) = 6( x - 1) - x has all rela numbers as solution.

The expression 2x + 3(x - 2) = 6( x - 1) + x can be solved as

`\begin{gathered} 2x+3\mleft(x-2\mright)=6(x-1) \\ 2x+3x-6=6x-6 \\ 5x-6=6x-6 \\ -6+6=6x-5x \\ 0=x\text{ So, for }2x+3(x-2)=6(x-1),\text{ solution is x=0} \\ 2x+3x-1=6\mleft(x-1\mright)-x\text{ can be solved as} \\ 2x+3x-1=6(x-1)-x\text{ } \\ 5x-1=6x-6-x \\ 5x-1=5x-6 \\ -1=-6 \\ \text{Hence, }2x+3x-1=6(x-1)-x\text{ has no solution.} \end{gathered}`