Solve -7x-(-5x^41 )≤ -1

Question

Solve the inequality

0.143157 \leq x \leq 1.066318

Alternative Form

x \in [0.143157, 1.066318]

Evaluate

- 7 x - (- 5 x^{4} \times 1) \leq - 1

Simplify

More Steps

- 7 x + 5 x^{4} \leq - 1

Move the expression to the left side

- 7 x + 5 x^{4} - (- 1) \leq 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 7 x + 5 x^{4} + 1 \leq 0

Rewrite the expression

- 7 x + 5 x^{4} + 1 = 0

Find the critical values by solving the corresponding equation

x \approx 1.066318 x \approx 0.143157

Determine the test intervals using the critical values

x < 0.143157 0.143157 < x < 1.066318 x > 1.066318

Choose a value form each interval

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

To determine if x < 0.143157 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0.143157 is not a solution x_{2} = 1 x_{3} = 2

To determine if 0.143157 < x < 1.066318 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0.143157 is not a solution 0.143157 < x < 1.066318 is the solution x_{3} = 2

To determine if x > 1.066318 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < 0.143157 is not a solution 0.143157 < x < 1.066318 is the solution x > 1.066318 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

0.143157 \leq x \leq 1.066318 is the solution

Solution

0.143157 \leq x \leq 1.066318

Alternative Form

x \in [0.143157, 1.066318]

Show Solution