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
7<x<11+7
Alternative Form
x∈(7,11+7)
Evaluate
(x−7)2<11×(x−7)
Multiply the terms
More Steps
Evaluate
11×(x−7)
Use the the distributive property to expand the expression
11×x+11×(−7)
Multiply the numbers
11×x−711
(x−7)2<11×x−711
Move the expression to the left side
(x−7)2−(11×x−711)<0
Subtract the terms
More Steps
Evaluate
(x−7)2−(11×x−711)
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−7)2−11×x+711
Expand the expression
x2−14x+49−11×x+711
x2−14x+49−11×x+711<0
Rewrite the expression
x2−14x+49−11×x+711=0
Collect like terms by calculating the sum or difference of their coefficients
x2+(−14−11)x+49+711=0
Expand the expression
x2−14x−11×x+49+711=0
Factor the expression
More Steps
Evaluate
x2−14x−11×x+49+711
Calculate
x2−7x−11×x+711−7x+49
Rewrite the expression
x×x−x×7−11×x+11×7−7x+7×7
Factor out x from the expression
x(x−7)−11×x+11×7−7x+7×7
Factor out −11 from the expression
x(x−7)−11×(x−7)−7x+7×7
Factor out −7 from the expression
x(x−7)−11×(x−7)−7(x−7)
Factor out x−7 from the expression
(x−11−7)(x−7)
(x−11−7)(x−7)=0
When the product of factors equals 0,at least one factor is 0
x−11−7=0x−7=0
Solve the equation for x
More Steps
Evaluate
x−11−7=0
Move the constant to the right-hand side and change its sign
x=0+11+7
Removing 0 doesn't change the value,so remove it from the expression
x=11+7
x=11+7x−7=0
Solve the equation for x
More Steps
Evaluate
x−7=0
Move the constant to the right-hand side and change its sign
x=0+7
Removing 0 doesn't change the value,so remove it from the expression
x=7
x=11+7x=7
Determine the test intervals using the critical values
x<77<x<11+7x>11+7
Choose a value form each interval
x1=6x2=9x3=11
To determine if x<7 is the solution to the inequality,test if the chosen value x=6 satisfies the initial inequality
More Steps
Evaluate
(6−7)2<11×6−711
Simplify
More Steps
Evaluate
(6−7)2
Subtract the numbers
(−1)2
Evaluate the power
1
1<11×6−711
Simplify
More Steps
Evaluate
11×6−711
Multiply the numbers
611−711
Rewrite the expression
(6−7)11
Subtract the numbers
−11
1<−11
Calculate
1<−3.316625
Check the inequality
false
x<7 is not a solutionx2=9x3=11
To determine if 7<x<11+7 is the solution to the inequality,test if the chosen value x=9 satisfies the initial inequality
More Steps
Evaluate
(9−7)2<11×9−711
Subtract the numbers
22<11×9−711
Simplify
More Steps
Evaluate
11×9−711
Multiply the numbers
911−711
Collect like terms by calculating the sum or difference of their coefficients
(9−7)11
Subtract the numbers
211
22<211
Calculate
4<211
Calculate
4<6.63325
Check the inequality
true
x<7 is not a solution7<x<11+7 is the solutionx3=11
To determine if x>11+7 is the solution to the inequality,test if the chosen value x=11 satisfies the initial inequality
More Steps
Evaluate
(11−7)2<11×11−711
Subtract the numbers
42<11×11−711
Simplify
More Steps
Evaluate
11×11−711
Multiply the numbers
1111−711
Collect like terms by calculating the sum or difference of their coefficients
(11−7)11
Subtract the numbers
411
42<411
Calculate
16<411
Calculate
16<13.266499
Check the inequality
false
x<7 is not a solution7<x<11+7 is the solutionx>11+7 is not a solution
Solution
7<x<11+7
Alternative Form
x∈(7,11+7)
Show Solution
