Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
0≤x<4
Alternative Form
x∈[0,4)
Evaluate
x−1<5−x
Find the domain
More Steps
Evaluate
{x≥05−x≥0
Calculate
More Steps
Evaluate
5−x≥0
Move the constant to the right side
−x≥0−5
Removing 0 doesn't change the value,so remove it from the expression
−x≥−5
Change the signs on both sides of the inequality and flip the inequality sign
x≤5
{x≥0x≤5
Find the intersection
0≤x≤5
x−1<5−x,0≤x≤5
Swap the sides
5−x>x−1
Separate the inequality into 2 possible cases
5−x>x−1,x−1≥05−x>x−1,x−1<0
Solve the inequality
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Solve the inequality
5−x>x−1
Square both sides of the inequality
5−x>(x−1)2
Move the expression to the left side
5−x−(x−1)2>0
Calculate
More Steps
Evaluate
5−x−(x−1)2
Simplify
5−x−x+2x−1
Subtract the numbers
4−x−x+2x
Subtract the terms
4−2x+2x
4−2x+2x>0
Move the expression to the right side
2x>−4+2x
Divide both sides
x>−2+x
Separate the inequality into 2 possible cases
x>−2+x,−2+x≥0x>−2+x,−2+x<0
Solve the inequality
More Steps
Solve the inequality
x>−2+x
Square both sides of the inequality
x>(−2+x)2
Expand the expression
x>4−4x+x2
Move the expression to the left side
x−(4−4x+x2)>0
Subtract the terms
5x−4−x2>0
Move the constant to the right side
5x−x2>0−(−4)
Add the terms
5x−x2>4
Evaluate
x2−5x<−4
Add the same value to both sides
x2−5x+425<−4+425
Evaluate
x2−5x+425<49
Evaluate
(x−25)2<49
Take the 2-th root on both sides of the inequality
(x−25)2<49
Calculate
x−25<23
Separate the inequality into 2 possible cases
{x−25<23x−25>−23
Calculate
{x<4x−25>−23
Calculate
{x<4x>1
Find the intersection
1<x<4
1<x<4,−2+x≥0x>−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
1<x<4,x≥2x>−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 true for any value of x
1<x<4,x≥2x∈R,−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
1<x<4,x≥2x∈R,x<2
Find the intersection
2≤x<4x∈R,x<2
Find the intersection
2≤x<4x<2
Find the union
x<4
x<4,x−1≥05−x>x−1,x−1<0
Solve the inequality
More Steps
Evaluate
x−1≥0
Add or subtract both sides
x≥0+1
Removing 0 doesn't change the value,so remove it from the expression
x≥1
Raise both sides of the inequality to the power of 2
x≥1
x<4,x≥15−x>x−1,x−1<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
x<4,x≥1x∈R,x−1<0
Solve the inequality
More Steps
Evaluate
x−1<0
Add or subtract both sides
x<0+1
Removing 0 doesn't change the value,so remove it from the expression
x<1
Raise both sides of the inequality to the power of 2
x<1
x<4,x≥1x∈R,x<1
Find the intersection
1≤x<4x∈R,x<1
Find the intersection
1≤x<4x<1
Find the union
x<4
Check if the solution is in the defined range
x<4,0≤x≤5
Solution
0≤x<4
Alternative Form
x∈[0,4)
Show Solution
