Solve w* w<6/2 - ScanMath

Evaluate

w \times w < \frac{6}{2}

Multiply the terms

w^{2} < \frac{6}{2}

Divide the terms

More Steps

w^{2} < 3

Move the expression to the left side

w^{2} - 3 < 0

Rewrite the expression

w^{2} - 3 = 0

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

w^{2} = 0 + 3

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

w^{2} = 3

Take the root of both sides of the equation and remember to use both positive and negative roots

w = \pm 3

Separate the equation into 2 possible cases

w = 3 w = - 3

Determine the test intervals using the critical values

w < - 3 - 3 < w < 3 w > 3

Choose a value form each interval

w_{1} = - 3 w_{2} = 0 w_{3} = 3

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

More Steps

w < - 3 is not a solution w_{2} = 0 w_{3} = 3

To determine if - 3 < w < 3 is the solution to the inequality,test if the chosen value w = 0 satisfies the initial inequality

More Steps

w < - 3 is not a solution - 3 < w < 3 is the solution w_{3} = 3

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

More Steps

w < - 3 is not a solution - 3 < w < 3 is the solution w > 3 is not a solution

Solution

- 3 < w < 3

Alternative Form

w \in (- 3, 3)

Solve the inequality