Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for k
k∈(−∞,−2)∪(2,+∞)
Evaluate
4k2>8
Calculate the absolute value
More Steps

Calculate
4k2
Rewrite the expression
4k2
Simplify
4k2
4k2>8
Move the expression to the left side
4k2−8>0
Rewrite the expression
4k2−8=0
Move the constant to the right-hand side and change its sign
4k2=0+8
Removing 0 doesn't change the value,so remove it from the expression
4k2=8
Divide both sides
44k2=48
Divide the numbers
k2=48
Divide the numbers
More Steps

Evaluate
48
Reduce the numbers
12
Calculate
2
k2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
k=±2
Separate the equation into 2 possible cases
k=2k=−2
Determine the test intervals using the critical values
k<−2−2<k<2k>2
Choose a value form each interval
k1=−2k2=0k3=2
To determine if k<−2 is the solution to the inequality,test if the chosen value k=−2 satisfies the initial inequality
More Steps

Evaluate
4(−2)2>8
Multiply the terms
More Steps

Evaluate
4(−2)2
Evaluate the power
4×4
Multiply the numbers
16
16>8
Check the inequality
true
k<−2 is the solutionk2=0k3=2
To determine if −2<k<2 is the solution to the inequality,test if the chosen value k=0 satisfies the initial inequality
More Steps

Evaluate
4×02>8
Simplify
More Steps

Evaluate
4×02
Calculate
4×0
Any expression multiplied by 0 equals 0
0
0>8
Check the inequality
false
k<−2 is the solution−2<k<2 is not a solutionk3=2
To determine if k>2 is the solution to the inequality,test if the chosen value k=2 satisfies the initial inequality
More Steps

Evaluate
4×22>8
Multiply the terms
More Steps

Evaluate
4×22
Rewrite the expression
22×22
Rewrite the expression
22+2
Calculate
24
24>8
Calculate
16>8
Check the inequality
true
k<−2 is the solution−2<k<2 is not a solutionk>2 is the solution
Solution
k∈(−∞,−2)∪(2,+∞)
Show Solution
