Question

1. Solve the inequality.

6x^2 - x < 2



Show your answer on a number line. State your answer in interval notation.

Answer 1

The answer in interval notation is
`\left(-(1)/(2),\:(2)/(3)\right)`

Explanation:

Consider the provided inequality.

`6x^2 - x < 2`

Subtract 2 from both sides.

`6x^2-x-2<0`

`6x^2+3x-4x-2<0`

`3x(2x+1)-2(2x+1)<0`

`(3x-2)(2x+1)<0`

`x<(2)/(3)\ or\ x<(-1)/(2)`

The value of function
`(3x-2)(2x+1)<0` is positive for
`x<-(1)/(2)`

The value function
`(3x-2)(2x+1)<0` is zero at
`x=-(1)/(2)`

The value function
`(3x-2)(2x+1)<0` is negative for
`-(1)/(2)<x<(2)/(3)`

The value function
`(3x-2)(2x+1)<0` is zero at
`x=(2)/(3)`

The value function
`(3x-2)(2x+1)<0` is positive for
`x>(2)/(3)`

Since we want the value of function less than 0, so the required interval which satisfy the condition < 0 is:

`-(1)/(2)<x<(2)/(3)`

The required number line is shown below:

The answer in interval notation is
`\left(-(1)/(2),\:(2)/(3)\right)`