Solve 4r^2>18 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for r

r \in (- \infty, - \frac{3 2}{2}) \cup (\frac{3 2}{2}, + \infty)

Evaluate

4 r^{2} > 18

Move the expression to the left side

4 r^{2} - 18 > 0

Rewrite the expression

4 r^{2} - 18 = 0

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

4 r^{2} = 0 + 18

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

4 r^{2} = 18

Divide both sides

\frac{4 r ^{2}}{4} = \frac{18}{4}

Divide the numbers

r^{2} = \frac{18}{4}

Cancel out the common factor 2

r^{2} = \frac{9}{2}

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

r = \pm \frac{9}{2}

Simplify the expression

More Steps

r = \pm \frac{3 2}{2}

Separate the equation into 2 possible cases

r = \frac{3 2}{2} r = - \frac{3 2}{2}

Determine the test intervals using the critical values

r < - \frac{3 2}{2} - \frac{3 2}{2} < r < \frac{3 2}{2} r > \frac{3 2}{2}

Choose a value form each interval

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

To determine if r < - \frac{3 2}{2} is the solution to the inequality,test if the chosen value r = - 3 satisfies the initial inequality

More Steps

r < - \frac{3 2}{2} is the solution r_{2} = 0 r_{3} = 3

To determine if - \frac{3 2}{2} < r < \frac{3 2}{2} is the solution to the inequality,test if the chosen value r = 0 satisfies the initial inequality

More Steps

r < - \frac{3 2}{2} is the solution - \frac{3 2}{2} < r < \frac{3 2}{2} is not a solution r_{3} = 3

To determine if r > \frac{3 2}{2} is the solution to the inequality,test if the chosen value r = 3 satisfies the initial inequality

More Steps

r < - \frac{3 2}{2} is the solution - \frac{3 2}{2} < r < \frac{3 2}{2} is not a solution r > \frac{3 2}{2} is the solution

Solution

r \in (- \infty, - \frac{3 2}{2}) \cup (\frac{3 2}{2}, + \infty)

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