Question
Solve the inequality
x>0
Alternative Form
x∈(0,+∞)
Evaluate
−3x<(8×32x)<3214x
Separate into two inequalities
{−3x<8×32x8×32x<3214x
Solve the inequality
More Steps

Evaluate
−3x<8×32x
Multiply the terms
More Steps

Multiply the terms
8×32x
Cancel out the common factor 8
1×4x
Multiply the terms
4x
−3x<4x
Cross multiply
−3x×4<x
Simplify the equation
−12x<x
Add or subtract both sides
−12x−x<0
Subtract the terms
More Steps

Evaluate
−12x−x
Collect like terms by calculating the sum or difference of their coefficients
(−12−1)x
Subtract the numbers
−13x
−13x<0
Change the signs on both sides of the inequality and flip the inequality sign
13x>0
Rewrite the expression
x>0
{x>08×32x<3214x
Solve the inequality
More Steps

Evaluate
8×32x<3214x
Multiply the terms
More Steps

Multiply the terms
8×32x
Cancel out the common factor 8
1×4x
Multiply the terms
4x
4x<3214x
Cancel out the common factor 2
4x<167x
Rewrite the expression
4x<167x
Cross multiply
x×16<4×7x
Simplify the equation
16x<4×7x
Simplify the equation
16x<28x
Add or subtract both sides
16x−28x<0
Subtract the terms
More Steps

Evaluate
16x−28x
Collect like terms by calculating the sum or difference of their coefficients
(16−28)x
Subtract the numbers
−12x
−12x<0
Change the signs on both sides of the inequality and flip the inequality sign
12x>0
Rewrite the expression
x>0
{x>0x>0
Solution
x>0
Alternative Form
x∈(0,+∞)
Show Solution
