Solve u*u 16<15 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for u

- \frac{15}{4} < u < \frac{15}{4}

Alternative Form

u \in (- \frac{15}{4}, \frac{15}{4})

Evaluate

u \times u \times 16 < 15

Multiply

More Steps

16 u^{2} < 15

Move the expression to the left side

16 u^{2} - 15 < 0

Rewrite the expression

16 u^{2} - 15 = 0

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

16 u^{2} = 0 + 15

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

16 u^{2} = 15

Divide both sides

\frac{16 u ^{2}}{16} = \frac{15}{16}

Divide the numbers

u^{2} = \frac{15}{16}

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

u = \pm \frac{15}{16}

Simplify the expression

More Steps

u = \pm \frac{15}{4}

Separate the equation into 2 possible cases

u = \frac{15}{4} u = - \frac{15}{4}

Determine the test intervals using the critical values

u < - \frac{15}{4} - \frac{15}{4} < u < \frac{15}{4} u > \frac{15}{4}

Choose a value form each interval

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

To determine if u < - \frac{15}{4} is the solution to the inequality,test if the chosen value u = - 2 satisfies the initial inequality

More Steps

u < - \frac{15}{4} is not a solution u_{2} = 0 u_{3} = 2

To determine if - \frac{15}{4} < u < \frac{15}{4} is the solution to the inequality,test if the chosen value u = 0 satisfies the initial inequality

More Steps

u < - \frac{15}{4} is not a solution - \frac{15}{4} < u < \frac{15}{4} is the solution u_{3} = 2

To determine if u > \frac{15}{4} is the solution to the inequality,test if the chosen value u = 2 satisfies the initial inequality

More Steps

u < - \frac{15}{4} is not a solution - \frac{15}{4} < u < \frac{15}{4} is the solution u > \frac{15}{4} is not a solution

Solution

- \frac{15}{4} < u < \frac{15}{4}

Alternative Form

u \in (- \frac{15}{4}, \frac{15}{4})

Show Solution