Question
Solve the system of inequalities
x>0
Alternative Form
x∈(0,+∞)
Evaluate
{2x−x×14×(x−5)≥x1x>0
Find the domain
More Steps

Evaluate
{x×1=0x=0
Any expression multiplied by 1 remains the same
{x=0x=0
Find the intersection
x=0
{2x−x×14×(x−5)≥x1x>0,x=0
Solve the inequality
More Steps

Evaluate
2x−x×14×(x−5)≥x1
Simplify
More Steps

Evaluate
2x−x×14×(x−5)
Any expression multiplied by 1 remains the same
2x−x4×(x−5)
Multiply the terms
2x−x4(x−5)
2x−x4(x−5)≥x1
Convert the expressions
x2x2−4x+20≥x1
Move the expression to the left side
x2x2−4x+20−x1≥0
Subtract the terms
More Steps

Evaluate
x2x2−4x+20−x1
Write all numerators above the common denominator
x2x2−4x+20−1
Subtract the numbers
x2x2−4x+19
x2x2−4x+19≥0
Separate the inequality into 2 possible cases
{2x2−4x+19≥0x>0{2x2−4x+19≤0x<0
Solve the inequality
More Steps

Evaluate
2x2−4x+19≥0
Move the constant to the right side
2x2−4x≥0−19
Add the terms
2x2−4x≥−19
Evaluate
x2−2x≥−219
Add the same value to both sides
x2−2x+1≥−219+1
Evaluate
x2−2x+1≥−217
Evaluate
(x−1)2≥−217
Calculate
x∈R
{x∈Rx>0{2x2−4x+19≤0x<0
Solve the inequality
More Steps

Evaluate
2x2−4x+19≤0
Move the constant to the right side
2x2−4x≤0−19
Add the terms
2x2−4x≤−19
Evaluate
x2−2x≤−219
Add the same value to both sides
x2−2x+1≤−219+1
Evaluate
x2−2x+1≤−217
Evaluate
(x−1)2≤−217
Calculate
x∈/R
{x∈Rx>0{x∈/Rx<0
Find the intersection
x>0{x∈/Rx<0
Find the intersection
x>0x∈/R
Find the union
x>0
{x>0x>0
Find the intersection
x>0
Check if the solution is in the defined range
x>0,x=0
Solution
x>0
Alternative Form
x∈(0,+∞)
Show Solution
