Solve 2a^4≤6 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for a

- 43 \leq a \leq 43

Alternative Form

a \in [- 43, 43]

Evaluate

2 a^{4} \leq 6

Move the expression to the left side

2 a^{4} - 6 \leq 0

Rewrite the expression

2 a^{4} - 6 = 0

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

2 a^{4} = 0 + 6

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

2 a^{4} = 6

Divide both sides

\frac{2 a ^{4}}{2} = \frac{6}{2}

Divide the numbers

a^{4} = \frac{6}{2}

Divide the numbers

More Steps

a^{4} = 3

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

a = \pm 43

Separate the equation into 2 possible cases

a = 43 a = - 43

Determine the test intervals using the critical values

a < - 43 - 43 < a < 43 a > 43

Choose a value form each interval

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

To determine if a < - 43 is the solution to the inequality,test if the chosen value a = - 2 satisfies the initial inequality

More Steps

a < - 43 is not a solution a_{2} = 0 a_{3} = 2

To determine if - 43 < a < 43 is the solution to the inequality,test if the chosen value a = 0 satisfies the initial inequality

More Steps

a < - 43 is not a solution - 43 < a < 43 is the solution a_{3} = 2

To determine if a > 43 is the solution to the inequality,test if the chosen value a = 2 satisfies the initial inequality

More Steps

a < - 43 is not a solution - 43 < a < 43 is the solution a > 43 is not a solution

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

- 43 \leq a \leq 43 is the solution

Solution

- 43 \leq a \leq 43

Alternative Form

a \in [- 43, 43]

Show Solution