Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x∈R
Alternative Form
All real solution
Evaluate
x2+2x<1
Move the expression to the left side
x2+2x−1<0
Subtract the terms
More Steps
Evaluate
x2+2x−1
Reduce fractions to a common denominator
x2+2x−x2+2x2+2
Write all numerators above the common denominator
x2+2x−(x2+2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2+2x−x2−2
x2+2x−x2−2<0
Set the numerator and denominator of x2+2x−x2−2 equal to 0 to find the values of x where sign changes may occur
x−x2−2=0x2+2=0
Calculate
More Steps
Evaluate
x−x2−2=0
Add or subtract both sides
x−x2=2
Divide both sides
−1x−x2=−12
Evaluate
−x+x2=−2
Add the same value to both sides
−x+x2+41=−2+41
Simplify the expression
(x−21)2=−47
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈/R
x∈/Rx2+2=0
Calculate
More Steps
Evaluate
x2+2=0
Move the constant to the right-hand side and change its sign
x2=0−2
Removing 0 doesn't change the value,so remove it from the expression
x2=−2
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x
x∈/R
x∈/Rx∈/R
There are no key numbers,so choose any value to test,for example x=0
x=0
Solution
More Steps
Evaluate
02+20<1
Simplify
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Evaluate
02+20
Calculate
0+20
Removing 0 doesn't change the value,so remove it from the expression
20
Divide the terms
0
0<1
Check the inequality
true
x∈R
Alternative Form
All real solution
Show Solution
