Solve x^(2) 4x-4≥0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \geq 1

Alternative Form

x \in [1, + \infty)

Evaluate

x^{2} \times 4 x - 4 \geq 0

Multiply

More Steps

Evaluate

x^{2} \times 4 x

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 4

Add the numbers

x^{3} \times 4

Use the commutative property to reorder the terms

4 x^{3}

4 x^{3} - 4 \geq 0

Rewrite the expression

4 x^{3} - 4 = 0

Move the constant to the right-hand side and change its sign

4 x^{3} = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

4 x^{3} = 4

Divide both sides

\frac{4 x ^{3}}{4} = \frac{4}{4}

Divide the numbers

x^{3} = \frac{4}{4}

Divide the numbers

More Steps

Evaluate

\frac{4}{4}

Reduce the numbers

\frac{1}{1}

Calculate

1

x^{3} = 1

Take the 3 -th root on both sides of the equation

3 x^{3} = 31

Calculate

x = 31

Simplify the root

x = 1

Determine the test intervals using the critical values

x < 1 x > 1

Choose a value form each interval

x_{1} = 0 x_{2} = 2

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

More Steps

Evaluate

4 \times 0^{3} - 4 \geq 0

Simplify

More Steps

Evaluate

4 \times 0^{3} - 4

Calculate

4 \times 0 - 4

Any expression multiplied by 0 equals 0

0 - 4

Removing 0 doesn't change the value,so remove it from the expression

- 4

- 4 \geq 0

Check the inequality

false

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

To determine if x > 1 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

Evaluate

4 \times 2^{3} - 4 \geq 0

Simplify

More Steps

Evaluate

4 \times 2^{3} - 4

Multiply the terms

2^{5} - 4

Evaluate the power

32 - 4

Subtract the numbers

28

28 \geq 0

Check the inequality

true

x < 1 is not a solution x > 1 is the solution

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

x \geq 1 is the solution

Solution

x \geq 1

Alternative Form

x \in [1, + \infty)

Show Solution