Solve 2x^2 -3≥4

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - \frac{14}{2}] \cup [\frac{14}{2}, + \infty)

Evaluate

2 x^{2} - 3 \geq 4

Move the expression to the left side

2 x^{2} - 3 - 4 \geq 0

Subtract the numbers

2 x^{2} - 7 \geq 0

Rewrite the expression

2 x^{2} - 7 = 0

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

2 x^{2} = 0 + 7

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

2 x^{2} = 7

Divide both sides

\frac{2 x ^{2}}{2} = \frac{7}{2}

Divide the numbers

x^{2} = \frac{7}{2}

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

x = \pm \frac{7}{2}

Simplify the expression

More Steps

x = \pm \frac{14}{2}

Separate the equation into 2 possible cases

x = \frac{14}{2} x = - \frac{14}{2}

Determine the test intervals using the critical values

x < - \frac{14}{2} - \frac{14}{2} < x < \frac{14}{2} x > \frac{14}{2}

Choose a value form each interval

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

To determine if x < - \frac{14}{2} is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - \frac{14}{2} is the solution x_{2} = 0 x_{3} = 3

To determine if - \frac{14}{2} < x < \frac{14}{2} is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - \frac{14}{2} is the solution - \frac{14}{2} < x < \frac{14}{2} is not a solution x_{3} = 3

To determine if x > \frac{14}{2} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - \frac{14}{2} is the solution - \frac{14}{2} < x < \frac{14}{2} is not a solution x > \frac{14}{2} is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \leq - \frac{14}{2} is the solution x \geq \frac{14}{2} is the solution

Solution

x \in (- \infty, - \frac{14}{2}] \cup [\frac{14}{2}, + \infty)

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