Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
0<x<31
Alternative Form
x∈(0,31)
Evaluate
3x×1>3x
Find the domain
More Steps
Evaluate
3x×1≥0
Multiply the terms
3x≥0
Rewrite the expression
x≥0
3x×1>3x,x≥0
Multiply the terms
3x>3x
Separate the inequality into 2 possible cases
3x>3x,3x≥03x>3x,3x<0
Solve the inequality
More Steps
Solve the inequality
3x>3x
Square both sides of the inequality
3x>(3x)2
Evaluate the power
More Steps
Evaluate
(3x)2
To raise a product to a power,raise each factor to that power
32x2
Evaluate the power
9x2
3x>9x2
Add or subtract both sides
3x−9x2>0
Evaluate
x2−31x<0
Add the same value to both sides
x2−31x+361<361
Evaluate
(x−61)2<361
Take the 2-th root on both sides of the inequality
(x−61)2<361
Calculate
x−61<61
Separate the inequality into 2 possible cases
{x−61<61x−61>−61
Calculate
More Steps
Evaluate
x−61<61
Move the constant to the right side
x<61+61
Add the numbers
x<31
{x<31x−61>−61
Cancel equal terms on both sides of the expression
{x<31x>0
Find the intersection
0<x<31
0<x<31,3x≥03x>3x,3x<0
Solve the inequality
0<x<31,x≥03x>3x,3x<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of x
0<x<31,x≥0x∈R,3x<0
Solve the inequality
0<x<31,x≥0x∈R,x<0
Find the intersection
0<x<31x∈R,x<0
Find the intersection
0<x<31x<0
Find the union
x∈(−∞,0)∪(0,31)
Check if the solution is in the defined range
x∈(−∞,0)∪(0,31),x≥0
Solution
0<x<31
Alternative Form
x∈(0,31)
Show Solution
