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
Solve for x
−5<x<2
Alternative Form
x∈(−5,2)
Evaluate
x2<10−3x
Move the expression to the left side
x2−(10−3x)<0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−10+3x<0
Rewrite the expression
x2−10+3x=0
Factor the expression
More Steps
Evaluate
x2−10+3x
Reorder the terms
x2+3x−10
Rewrite the expression
x2+(5−2)x−10
Calculate
x2+5x−2x−10
Rewrite the expression
x×x+x×5−2x−2×5
Factor out x from the expression
x(x+5)−2x−2×5
Factor out −2 from the expression
x(x+5)−2(x+5)
Factor out x+5 from the expression
(x−2)(x+5)
(x−2)(x+5)=0
When the product of factors equals 0,at least one factor is 0
x−2=0x+5=0
Solve the equation for x
More Steps
Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x+5=0
Solve the equation for x
More Steps
Evaluate
x+5=0
Move the constant to the right-hand side and change its sign
x=0−5
Removing 0 doesn't change the value,so remove it from the expression
x=−5
x=2x=−5
Determine the test intervals using the critical values
x<−5−5<x<2x>2
Choose a value form each interval
x1=−6x2=−2x3=3
To determine if x<−5 is the solution to the inequality,test if the chosen value x=−6 satisfies the initial inequality
More Steps
Evaluate
(−6)2<10−3(−6)
Simplify
More Steps
Evaluate
10−3(−6)
Multiply the numbers
10−(−18)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
10+18
Add the numbers
28
(−6)2<28
Calculate
62<28
Calculate
36<28
Check the inequality
false
x<−5 is not a solutionx2=−2x3=3
To determine if −5<x<2 is the solution to the inequality,test if the chosen value x=−2 satisfies the initial inequality
More Steps
Evaluate
(−2)2<10−3(−2)
Simplify
More Steps
Evaluate
10−3(−2)
Multiply the numbers
10−(−6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
10+6
Add the numbers
16
(−2)2<16
Calculate
22<16
Calculate
4<16
Check the inequality
true
x<−5 is not a solution−5<x<2 is the solutionx3=3
To determine if x>2 is the solution to the inequality,test if the chosen value x=3 satisfies the initial inequality
More Steps
Evaluate
32<10−3×3
Simplify
More Steps
Evaluate
10−3×3
Multiply the numbers
10−9
Subtract the numbers
1
32<1
Calculate
9<1
Check the inequality
false
x<−5 is not a solution−5<x<2 is the solutionx>2 is not a solution
Solution
−5<x<2
Alternative Form
x∈(−5,2)
Show Solution
