Question

1. Solve -4x < -3(6x - 2) and sketch the solution set on a number line.

Answer 1

We need to solve the inequality:

`-4x<-3\mleft(6x-2\mright)`

Let's multiply right side out and take variables to one side and numbers to another. The process is shown below:

`\begin{gathered} -4x<-3\mleft(6x-2\mright) \\ -4x<-18x+6 \\ -4x+18x<6 \\ 14x<6 \\ x<(6)/(14) \\ x<(3)/(7) \end{gathered}`

The solution set is:

`\begin{gathered} x<(3)/(7) \\ or \\ x<0.4286 \end{gathered}`

This means that x is less than 3/7, or

x is less than 0.4286

On the number line it looks: