Question

Solve the following inequality. use interval notation to write the solution set. 2x - 3 < 6x - 11

Answer 1

Wfite out the inequality

`2x-3<6x-11`

subtract 6x from both sides

`\begin{gathered} 2x-6x-3<6x-6x-11 \\ -4x-3<-11 \end{gathered}`

Add 3 to both sides, we have

`\begin{gathered} -4x-3+3<-11+3 \\ \text{then} \\ -4x<-8 \end{gathered}`

Divide both sides by -4 and revert the inequality sign

We obtain

`\begin{gathered} -(4x)/(-4)<-(8)/(-4) \\ \text{Then} \\ x>2 \end{gathered}`

Therefore

The solution to the inequality is x>2

In interval notation we have

`\mleft(2,\: \infty\: \mright)`

Answer: (2,∞)