Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
0<y<2
Alternative Form
y∈(0,2)
Evaluate
2y−6<y2<2y
Separate into two inequalities
{2y−6<y2y2<2y
Solve the inequality
More Steps
Evaluate
2y−6<y2
Move the expression to the left side
2y−6−y2<0
Move the constant to the right side
2y−y2<0−(−6)
Add the terms
2y−y2<6
Evaluate
y2−2y>−6
Add the same value to both sides
y2−2y+1>−6+1
Evaluate
y2−2y+1>−5
Evaluate
(y−1)2>−5
Calculate
y∈R
{y∈Ry2<2y
Solve the inequality
More Steps
Evaluate
y2<2y
Move the expression to the left side
y2−2y<0
Add the same value to both sides
y2−2y+1<1
Evaluate
(y−1)2<1
Take the 2-th root on both sides of the inequality
(y−1)2<1
Calculate
∣y−1∣<1
Separate the inequality into 2 possible cases
{y−1<1y−1>−1
Calculate
More Steps
Evaluate
y−1<1
Move the constant to the right side
y<1+1
Add the numbers
y<2
{y<2y−1>−1
Cancel equal terms on both sides of the expression
{y<2y>0
Find the intersection
0<y<2
{y∈R0<y<2
Solution
0<y<2
Alternative Form
y∈(0,2)
Show Solution
