Question

Solve the inequality. Write the solution in both interval notation and graphically.

Answer 1

Given:

`(3)/(4)(x-2)\text{ }<\text{ x -2}`

Opening the bracket:

`(3x)/(4)\text{ - }(6)/(4)\text{ }<\text{ x - 2}`

Collect like terms:

`\begin{gathered} (3x)/(4)-x\text{ }<\text{ }(6)/(4)\text{ - 2} \\ (3x-4x)/(4)\text{ }<\text{ }(6-8)/(4) \\ -(x)/(4)\text{ }<\text{ }(-2)/(4) \end{gathered}`

Solving for x:

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

The solution in interval notation:

`(2\text{ , }\infty\text{ )}`

The solution on a graph:

The solution on a number line: