Question

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

Answer 1

SOLUTION

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

$\begin{gathered} -\frac{4x}{-4}<-\frac{8}{-4} \\ \text{Then} \\ x>2 \end{gathered}$

Therefore

The solution to the inequality is x>2

In interval notation we have

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

Answer: (2,∞)