Solve j*j8-15>-14

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for j

j \in (- \infty, - \frac{2}{4}) \cup (\frac{2}{4}, + \infty)

Evaluate

j \times j \times 8 - 15 > - 14

Multiply

More Steps

8 j^{2} - 15 > - 14

Move the expression to the left side

8 j^{2} - 15 - (- 14) > 0

Subtract the numbers

More Steps

8 j^{2} - 1 > 0

Rewrite the expression

8 j^{2} - 1 = 0

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

8 j^{2} = 0 + 1

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

8 j^{2} = 1

Divide both sides

\frac{8 j ^{2}}{8} = \frac{1}{8}

Divide the numbers

j^{2} = \frac{1}{8}

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

j = \pm \frac{1}{8}

Simplify the expression

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j = \pm \frac{2}{4}

Separate the equation into 2 possible cases

j = \frac{2}{4} j = - \frac{2}{4}

Determine the test intervals using the critical values

j < - \frac{2}{4} - \frac{2}{4} < j < \frac{2}{4} j > \frac{2}{4}

Choose a value form each interval

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

To determine if j < - \frac{2}{4} is the solution to the inequality,test if the chosen value j = - 1 satisfies the initial inequality

More Steps

j < - \frac{2}{4} is the solution j_{2} = 0 j_{3} = 1

To determine if - \frac{2}{4} < j < \frac{2}{4} is the solution to the inequality,test if the chosen value j = 0 satisfies the initial inequality

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j < - \frac{2}{4} is the solution - \frac{2}{4} < j < \frac{2}{4} is not a solution j_{3} = 1

To determine if j > \frac{2}{4} is the solution to the inequality,test if the chosen value j = 1 satisfies the initial inequality

More Steps

j < - \frac{2}{4} is the solution - \frac{2}{4} < j < \frac{2}{4} is not a solution j > \frac{2}{4} is the solution

Solution

j \in (- \infty, - \frac{2}{4}) \cup (\frac{2}{4}, + \infty)

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