Solve c*c85<4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for c

- \frac{2 85}{85} < c < \frac{2 85}{85}

Alternative Form

c \in (- \frac{2 85}{85}, \frac{2 85}{85})

Evaluate

c \times c \times 85 < 4

Multiply

More Steps

85 c^{2} < 4

Move the expression to the left side

85 c^{2} - 4 < 0

Rewrite the expression

85 c^{2} - 4 = 0

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

85 c^{2} = 0 + 4

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

85 c^{2} = 4

Divide both sides

\frac{85 c ^{2}}{85} = \frac{4}{85}

Divide the numbers

c^{2} = \frac{4}{85}

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

c = \pm \frac{4}{85}

Simplify the expression

More Steps

c = \pm \frac{2 85}{85}

Separate the equation into 2 possible cases

c = \frac{2 85}{85} c = - \frac{2 85}{85}

Determine the test intervals using the critical values

c < - \frac{2 85}{85} - \frac{2 85}{85} < c < \frac{2 85}{85} c > \frac{2 85}{85}

Choose a value form each interval

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

To determine if c < - \frac{2 85}{85} is the solution to the inequality,test if the chosen value c = - 1 satisfies the initial inequality

More Steps

c < - \frac{2 85}{85} is not a solution c_{2} = 0 c_{3} = 1

To determine if - \frac{2 85}{85} < c < \frac{2 85}{85} is the solution to the inequality,test if the chosen value c = 0 satisfies the initial inequality

More Steps

c < - \frac{2 85}{85} is not a solution - \frac{2 85}{85} < c < \frac{2 85}{85} is the solution c_{3} = 1

To determine if c > \frac{2 85}{85} is the solution to the inequality,test if the chosen value c = 1 satisfies the initial inequality

More Steps

c < - \frac{2 85}{85} is not a solution - \frac{2 85}{85} < c < \frac{2 85}{85} is the solution c > \frac{2 85}{85} is not a solution

Solution

- \frac{2 85}{85} < c < \frac{2 85}{85}

Alternative Form

c \in (- \frac{2 85}{85}, \frac{2 85}{85})

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