Solve 2t 8<4t^4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

t \in (- \infty, 0) \cup (34, + \infty)

Evaluate

2 t \times 8 < 4 t^{4}

Multiply the terms

16 t < 4 t^{4}

Move the expression to the left side

16 t - 4 t^{4} < 0

Rewrite the expression

16 t - 4 t^{4} = 0

Factor the expression

4 t (4 - t^{3}) = 0

Divide both sides

t (4 - t^{3}) = 0

Separate the equation into 2 possible cases

t = 0 4 - t^{3} = 0

Solve the equation

More Steps

t = 0 t = 34

Determine the test intervals using the critical values

t < 0 0 < t < 34 t > 34

Choose a value form each interval

t_{1} = - 1 t_{2} = 1 t_{3} = 3

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

More Steps

t < 0 is the solution t_{2} = 1 t_{3} = 3

To determine if 0 < t < 34 is the solution to the inequality,test if the chosen value t = 1 satisfies the initial inequality

More Steps

t < 0 is the solution 0 < t < 34 is not a solution t_{3} = 3

To determine if t > 34 is the solution to the inequality,test if the chosen value t = 3 satisfies the initial inequality

More Steps

t < 0 is the solution 0 < t < 34 is not a solution t > 34 is the solution

Solution

t \in (- \infty, 0) \cup (34, + \infty)

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