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1. Solve the inequality.

6x^2 - x < 2



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

1 Answer

6 votes

Answer:

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)

1. Solve the inequality. 6x^2 - x < 2 Show your answer on a number line. State-example-1

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