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
8<x<3+8
Alternative Form
x∈(8,3+8)
Evaluate
(x−8)2<3×(x−8)
Multiply the terms
More Steps
Evaluate
3×(x−8)
Use the the distributive property to expand the expression
3×x+3×(−8)
Multiply the numbers
3×x−83
(x−8)2<3×x−83
Move the expression to the left side
(x−8)2−(3×x−83)<0
Subtract the terms
More Steps
Evaluate
(x−8)2−(3×x−83)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
(x−8)2−3×x+83
Expand the expression
x2−16x+64−3×x+83
x2−16x+64−3×x+83<0
Rewrite the expression
x2−16x+64−3×x+83=0
Collect like terms by calculating the sum or difference of their coefficients
x2+(−16−3)x+64+83=0
Expand the expression
x2−16x−3×x+64+83=0
Factor the expression
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Evaluate
x2−16x−3×x+64+83
Calculate
x2−8x−3×x+83−8x+64
Rewrite the expression
x×x−x×8−3×x+3×8−8x+8×8
Factor out x from the expression
x(x−8)−3×x+3×8−8x+8×8
Factor out −3 from the expression
x(x−8)−3×(x−8)−8x+8×8
Factor out −8 from the expression
x(x−8)−3×(x−8)−8(x−8)
Factor out x−8 from the expression
(x−3−8)(x−8)
(x−3−8)(x−8)=0
When the product of factors equals 0,at least one factor is 0
x−3−8=0x−8=0
Solve the equation for x
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Evaluate
x−3−8=0
Move the constant to the right-hand side and change its sign
x=0+3+8
Removing 0 doesn't change the value,so remove it from the expression
x=3+8
x=3+8x−8=0
Solve the equation for x
More Steps
Evaluate
x−8=0
Move the constant to the right-hand side and change its sign
x=0+8
Removing 0 doesn't change the value,so remove it from the expression
x=8
x=3+8x=8
Determine the test intervals using the critical values
x<88<x<3+8x>3+8
Choose a value form each interval
x1=7x2=9x3=11
To determine if x<8 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
More Steps
Evaluate
(7−8)2<3×7−83
Simplify
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Evaluate
(7−8)2
Subtract the numbers
(−1)2
Evaluate the power
1
1<3×7−83
Simplify
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Evaluate
3×7−83
Multiply the numbers
73−83
Rewrite the expression
(7−8)3
Subtract the numbers
−3
1<−3
Calculate
1<−1.732051
Check the inequality
false
x<8 is not a solutionx2=9x3=11
To determine if 8<x<3+8 is the solution to the inequality,test if the chosen value x=9 satisfies the initial inequality
More Steps
Evaluate
(9−8)2<3×9−83
Simplify
More Steps
Evaluate
(9−8)2
Subtract the numbers
12
1 raised to any power equals to 1
1
1<3×9−83
Simplify
More Steps
Evaluate
3×9−83
Multiply the numbers
93−83
Collect like terms by calculating the sum or difference of their coefficients
(9−8)3
Subtract the numbers
3
1<3
Calculate
1<1.732051
Check the inequality
true
x<8 is not a solution8<x<3+8 is the solutionx3=11
To determine if x>3+8 is the solution to the inequality,test if the chosen value x=11 satisfies the initial inequality
More Steps
Evaluate
(11−8)2<3×11−83
Subtract the numbers
32<3×11−83
Simplify
More Steps
Evaluate
3×11−83
Multiply the numbers
113−83
Collect like terms by calculating the sum or difference of their coefficients
(11−8)3
Subtract the numbers
33
32<33
Calculate
9<33
Calculate
9<5.196152
Check the inequality
false
x<8 is not a solution8<x<3+8 is the solutionx>3+8 is not a solution
Solution
8<x<3+8
Alternative Form
x∈(8,3+8)
Show Solution
