Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−1.065642≤x≤1.065642
Alternative Form
x∈[−1.065642,1.065642]
Evaluate
∣x×1∣3x3≤6−2∣x×1∣
Simplify
More Steps
Evaluate
∣x×1∣3x3
Any expression multiplied by 1 remains the same
∣x∣3x3
Calculate the absolute value
∣x∣×3x3
Multiply the terms
3x4
3x4≤6−2∣x×1∣
Any expression multiplied by 1 remains the same
3x4≤6−2∣x∣
Move the expression to the left side
3x4−(6−2∣x∣)≤0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x4−6+2∣x∣≤0
Rearrange the terms
3x4+2∣x∣≤6
Separate the inequality into 2 possible cases
3x4+2x≤6,x≥03x4+2(−x)≤6,x<0
Evaluate
More Steps
Evaluate
3x4+2x≤6
Move the expression to the left side
3x4+2x−6≤0
Rewrite the expression
3x4+2x−6=0
Find the critical values by solving the corresponding equation
x≈1.065642x≈−1.301299
Determine the test intervals using the critical values
x<−1.301299−1.301299<x<1.065642x>1.065642
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−1.301299 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
3(−2)4+2(−2)−6≤0
Simplify
38≤0
Check the inequality
false
x<−1.301299 is not a solutionx2=0x3=2
To determine if −1.301299<x<1.065642 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
3×04+2×0−6≤0
Any expression multiplied by 0 equals 0
3×04+0−6≤0
Simplify
−6≤0
Check the inequality
true
x<−1.301299 is not a solution−1.301299<x<1.065642 is the solutionx3=2
To determine if x>1.065642 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
3×24+2×2−6≤0
Simplify
46≤0
Check the inequality
false
x<−1.301299 is not a solution−1.301299<x<1.065642 is the solutionx>1.065642 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−1.301299≤x≤1.065642 is the solution
The final solution of the original inequality is −1.301299≤x≤1.065642
−1.301299≤x≤1.065642
−1.301299≤x≤1.065642,x≥03x4+2(−x)≤6,x<0
Evaluate
More Steps
Evaluate
3x4+2(−x)≤6
Simplify the expression
3x4−2x≤6
Move the expression to the left side
3x4−2x−6≤0
Rewrite the expression
3x4−2x−6=0
Find the critical values by solving the corresponding equation
x≈1.301299x≈−1.065642
Determine the test intervals using the critical values
x<−1.065642−1.065642<x<1.301299x>1.301299
Choose a value form each interval
x1=−2x2=0x3=2
To determine if x<−1.065642 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
3(−2)4−2(−2)−6≤0
Simplify
46≤0
Check the inequality
false
x<−1.065642 is not a solutionx2=0x3=2
To determine if −1.065642<x<1.301299 is the solution to the inequality,test if the chosen value x=0 satisfies the initial inequality
More Steps
Evaluate
3×04−2×0−6≤0
Any expression multiplied by 0 equals 0
3×04−0−6≤0
Simplify
−6≤0
Check the inequality
true
x<−1.065642 is not a solution−1.065642<x<1.301299 is the solutionx3=2
To determine if x>1.301299 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps
Evaluate
3×24−2×2−6≤0
Simplify
38≤0
Check the inequality
false
x<−1.065642 is not a solution−1.065642<x<1.301299 is the solutionx>1.301299 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−1.065642≤x≤1.301299 is the solution
The final solution of the original inequality is −1.065642≤x≤1.301299
−1.065642≤x≤1.301299
−1.301299≤x≤1.065642,x≥0−1.065642≤x≤1.301299,x<0
Find the intersection
0≤x≤1.065642−1.065642≤x≤1.301299,x<0
Find the intersection
0≤x≤1.065642−1.065642≤x<0
Solution
−1.065642≤x≤1.065642
Alternative Form
x∈[−1.065642,1.065642]
Show Solution
