Question

DJ is solving the linear equation 18+7x-3=10x+15-3x. His final two steps follow. Select the statement that correctly interprets DJ's solution.A. The solution is x=0B. The solution is the ordered pair (15, 15)C. There are infinite solutions since 7x=7xD. There are no solutions since 7x≠7x

Answer 1

We are told that DJ was solving a linear equation

`\begin{gathered} 18+7x-3=10x+15-3x \\ \text{which becomes } \\ 18-3+7x=10x-3x+15\text{ when he collects like terms, then } \\ 15+7x=7x+15 \\ \text{subtracting 15 from both sides } \\ 15-15+7x=7x+15-15 \\ 0+7x=7x+0 \\ 7x=7x \end{gathered}`

So, DJ's solution was correct.

Now since he got

`7x=7x`

there are infinitely many solutions, because x can take any number.

Hence, there are infinite solutions since 7x = 7x

Therefore, the correct answer is option C