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
−3<x<5
Alternative Form
x∈(−3,5)
Evaluate
x2−15<2x
Move the expression to the left side
x2−15−2x<0
Rewrite the expression
x2−15−2x=0
Factor the expression
More Steps
Evaluate
x2−15−2x
Reorder the terms
x2−2x−15
Rewrite the expression
x2+(3−5)x−15
Calculate
x2+3x−5x−15
Rewrite the expression
x×x+x×3−5x−5×3
Factor out x from the expression
x(x+3)−5x−5×3
Factor out −5 from the expression
x(x+3)−5(x+3)
Factor out x+3 from the expression
(x−5)(x+3)
(x−5)(x+3)=0
When the product of factors equals 0,at least one factor is 0
x−5=0x+3=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=5x+3=0
Solve the equation for x
More Steps
Evaluate
x+3=0
Move the constant to the right-hand side and change its sign
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
x=5x=−3
Determine the test intervals using the critical values
x<−3−3<x<5x>5
Choose a value form each interval
x1=−4x2=1x3=6
To determine if x<−3 is the solution to the inequality,test if the chosen value x=−4 satisfies the initial inequality
More Steps
Evaluate
(−4)2−15<2(−4)
Subtract the numbers
More Steps
Evaluate
(−4)2−15
Simplify
42−15
Evaluate the power
16−15
Subtract the numbers
1
1<2(−4)
Multiply the numbers
More Steps
Evaluate
2(−4)
Multiplying or dividing an odd number of negative terms equals a negative
−2×4
Multiply the numbers
−8
1<−8
Check the inequality
false
x<−3 is not a solutionx2=1x3=6
To determine if −3<x<5 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
12−15<2×1
Simplify
More Steps
Evaluate
12−15
1 raised to any power equals to 1
1−15
Subtract the numbers
−14
−14<2×1
Any expression multiplied by 1 remains the same
−14<2
Check the inequality
true
x<−3 is not a solution−3<x<5 is the solutionx3=6
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
62−15<2×6
Subtract the numbers
More Steps
Evaluate
62−15
Evaluate the power
36−15
Subtract the numbers
21
21<2×6
Multiply the numbers
21<12
Check the inequality
false
x<−3 is not a solution−3<x<5 is the solutionx>5 is not a solution
Solution
−3<x<5
Alternative Form
x∈(−3,5)
Show Solution
