Solve c^27>9 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for c

c \in (- \infty, - \frac{3 7}{7}) \cup (\frac{3 7}{7}, + \infty)

Evaluate

c^{2} \times 7 > 9

Use the commutative property to reorder the terms

7 c^{2} > 9

Move the expression to the left side

7 c^{2} - 9 > 0

Rewrite the expression

7 c^{2} - 9 = 0

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

7 c^{2} = 0 + 9

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

7 c^{2} = 9

Divide both sides

\frac{7 c ^{2}}{7} = \frac{9}{7}

Divide the numbers

c^{2} = \frac{9}{7}

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

c = \pm \frac{9}{7}

Simplify the expression

More Steps

c = \pm \frac{3 7}{7}

Separate the equation into 2 possible cases

c = \frac{3 7}{7} c = - \frac{3 7}{7}

Determine the test intervals using the critical values

c < - \frac{3 7}{7} - \frac{3 7}{7} < c < \frac{3 7}{7} c > \frac{3 7}{7}

Choose a value form each interval

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

To determine if c < - \frac{3 7}{7} is the solution to the inequality,test if the chosen value c = - 2 satisfies the initial inequality

More Steps

c < - \frac{3 7}{7} is the solution c_{2} = 0 c_{3} = 2

To determine if - \frac{3 7}{7} < c < \frac{3 7}{7} is the solution to the inequality,test if the chosen value c = 0 satisfies the initial inequality

More Steps

c < - \frac{3 7}{7} is the solution - \frac{3 7}{7} < c < \frac{3 7}{7} is not a solution c_{3} = 2

To determine if c > \frac{3 7}{7} is the solution to the inequality,test if the chosen value c = 2 satisfies the initial inequality

More Steps

c < - \frac{3 7}{7} is the solution - \frac{3 7}{7} < c < \frac{3 7}{7} is not a solution c > \frac{3 7}{7} is the solution

Solution

c \in (- \infty, - \frac{3 7}{7}) \cup (\frac{3 7}{7}, + \infty)

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