Question

Can you check my work to make sure I did everything correctly?

Answer 1

`\begin{gathered} (3x-7)(x+1)=10x-2 \\ 3x^2+3x-7x-7=10x-2 \\ 3x^2+3x-7x-7-10x+2=0 \\ 3x^2-14x-5=0 \\ \text{let's use factorisation} \\ 3x^2-15x+x-5=0 \\ (3x^2-15x)+(x-5)=0 \\ 3x(x-5)+1(x-5)=0 \\ (3x+1)(x-5)=0 \\ 3x+1=0 \\ 3x=-1 \\ \text{Divide both sides by 3} \\ x=(-1)/(3) \\ \text{Then x-5=0} \\ x=5 \\ \text{The final answer is} \\ x=(-1)/(3)\text{ and x=5} \end{gathered}`

Therefore, the rational numbers are x = -1/3 and 5