Question

Can someone please help me with these? I tried doing them myself, but I got confused enough that I haven’t ended up with an answer yet

Answer 1

Given:

`1-3x>14-(4-6x)`

Solving the given inequality with the steps involved,

`\begin{gathered} 1-3x>14-(4-6x) \\ E\text{ xpanding the bracket on the r}ight\text{ hand side of the inequality;} \\ 1-3x>14-4+6x \\ 1-3x>10+6x \\ \text{Collecting the like terms;} \\ 1-10>6x+3x \\ -9>9x \\ \text{Dividing both sides by 9,} \\ -(9)/(9)>(9x)/(9) \\ -1>x \\ \text{Flipping the sides, and changing the inequality using the principle if a>b, then bx, } \\ \text{then} \\ x<-1 \end{gathered}`

Therefore, the solution as inequality is;

`x<-1`

The solution in interval notation therefore is;

`(-\infty,-1)`

Graphing the solution on a number line;