Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x≥0
Alternative Form
x∈[0,+∞)
Evaluate
3x−2<x
Find the domain
More Steps
Evaluate
3x≥0
Rewrite the expression
x≥0
3x−2<x,x≥0
Move the expression to the left side
3x−2−x<0
Move the expression to the right side
3x<2+x
Separate the inequality into 2 possible cases
3x<2+x,2+x≥03x<2+x,2+x<0
Solve the inequality
More Steps
Solve the inequality
3x<2+x
Square both sides of the inequality
3x<(2+x)2
Expand the expression
3x<4+4x+x2
Move the expression to the left side
3x−(4+4x+x2)<0
Subtract the terms
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Evaluate
3x−(4+4x+x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x−4−4x−x2
Subtract the terms
−x−4−x2
−x−4−x2<0
Move the constant to the right side
−x−x2<0−(−4)
Add the terms
−x−x2<4
Evaluate
x2+x>−4
Add the same value to both sides
x2+x+41>−4+41
Evaluate
x2+x+41>−415
Evaluate
(x+21)2>−415
Calculate
x∈R
x∈R,2+x≥03x<2+x,2+x<0
Solve the inequality
More Steps
Evaluate
2+x≥0
Move the constant to the right side
x≥0−2
Removing 0 doesn't change the value,so remove it from the expression
x≥−2
x∈R,x≥−23x<2+x,2+x<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈R,x≥−2x∈∅,2+x<0
Solve the inequality
More Steps
Evaluate
2+x<0
Move the constant to the right side
x<0−2
Removing 0 doesn't change the value,so remove it from the expression
x<−2
x∈R,x≥−2x∈∅,x<−2
Find the intersection
x≥−2x∈∅,x<−2
Find the intersection
x≥−2x∈∅
Find the union
x≥−2
Check if the solution is in the defined range
x≥−2,x≥0
Solution
x≥0
Alternative Form
x∈[0,+∞)
Show Solution
