Solve (12x-1)(3x 1)< 1 (6x^2)^2

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in (- \infty, - 1.039317) \cup (0, 0.083924) \cup (0.955393, + \infty)

Evaluate

(12 x - 1) (3 x \times 1) < 1 \times (6 x^{2})^{2}

Remove the parentheses

(12 x - 1) \times 3 x \times 1 < 1 \times (6 x^{2})^{2}

Multiply the terms

More Steps

3 (12 x - 1) x < 1 \times (6 x^{2})^{2}

Multiply the terms

More Steps

3 (12 x - 1) x < 36 x^{4}

Move the expression to the left side

3 (12 x - 1) x - 36 x^{4} < 0

Expand the expression

More Steps

36 x^{2} - 3 x - 36 x^{4} < 0

Rewrite the expression

36 x^{2} - 3 x - 36 x^{4} = 0

Factor the expression

3 x (12 x - 1 - 12 x^{3}) = 0

Divide both sides

x (12 x - 1 - 12 x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 12 x - 1 - 12 x^{3} = 0

Solve the equation

x = 0 x \approx - 1.039317 x \approx 0.083924 x \approx 0.955393

Determine the test intervals using the critical values

x < - 1.039317 - 1.039317 < x < 0 0 < x < 0.083924 0.083924 < x < 0.955393 x > 0.955393

Choose a value form each interval

x_{1} = - 2 x_{2} = - 1 x_{3} \approx 0.041962 x_{4} \approx 0.519659 x_{5} = 2

To determine if x < - 1.039317 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 1.039317 is the solution x_{2} = - 1 x_{3} \approx 0.041962 x_{4} \approx 0.519659 x_{5} = 2

To determine if - 1.039317 < x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 1.039317 is the solution - 1.039317 < x < 0 is not a solution x_{3} \approx 0.041962 x_{4} \approx 0.519659 x_{5} = 2

To determine if 0 < x < 0.083924 is the solution to the inequality,test if the chosen value x \approx 0.041962 satisfies the initial inequality

More Steps

x < - 1.039317 is the solution - 1.039317 < x < 0 is not a solution 0 < x < 0.083924 is the solution x_{4} \approx 0.519659 x_{5} = 2

To determine if 0.083924 < x < 0.955393 is the solution to the inequality,test if the chosen value x \approx 0.519659 satisfies the initial inequality

More Steps

x < - 1.039317 is the solution - 1.039317 < x < 0 is not a solution 0 < x < 0.083924 is the solution 0.083924 < x < 0.955393 is not a solution x_{5} = 2

To determine if x > 0.955393 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 1.039317 is the solution - 1.039317 < x < 0 is not a solution 0 < x < 0.083924 is the solution 0.083924 < x < 0.955393 is not a solution x > 0.955393 is the solution

Solution

x \in (- \infty, - 1.039317) \cup (0, 0.083924) \cup (0.955393, + \infty)

Show Solution