Solve x-1/5-4x^3/10<1-5x/25 - ScanMath

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Question

Solve the inequality

x > - 2.103803

Alternative Form

x \in (- 2.103803, + \infty)

Evaluate

x - \frac{1}{5} - (4 \times \frac{x ^{3}}{10}) < 1 - (5 \times \frac{x}{25})

Multiply the terms

More Steps

x - \frac{1}{5} - \frac{2 x ^{3}}{5} < 1 - (5 \times \frac{x}{25})

Multiply the terms

More Steps

x - \frac{1}{5} - \frac{2 x ^{3}}{5} < 1 - \frac{x}{5}

Multiply both sides of the inequality by 5

(x - \frac{1}{5} - \frac{2 x ^{3}}{5}) \times 5 < (1 - \frac{x}{5}) \times 5

Multiply the terms

More Steps

5 x - 1 - 2 x^{3} < (1 - \frac{x}{5}) \times 5

Multiply the terms

More Steps

5 x - 1 - 2 x^{3} < 5 - x

Move the expression to the left side

5 x - 1 - 2 x^{3} - (5 - x) < 0

Subtract the terms

More Steps

6 x - 6 - 2 x^{3} < 0

Rewrite the expression

6 x - 6 - 2 x^{3} = 0

Factor the expression

2 (3 x - 3 - x^{3}) = 0

Divide both sides

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

Calculate

x \approx - 2.103803

Determine the test intervals using the critical values

x < - 2.103803 x > - 2.103803

Choose a value form each interval

x_{1} = - 3 x_{2} = - 1

To determine if x < - 2.103803 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 2.103803 is not a solution x_{2} = - 1

To determine if x > - 2.103803 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < - 2.103803 is not a solution x > - 2.103803 is the solution

Solution

x > - 2.103803

Alternative Form

x \in (- 2.103803, + \infty)

Show Solution