Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for x
−3+4≤x≤3+4
Alternative Form
x∈[−3+4,3+4]
Evaluate
6x−x2−5≥8−2x
Move the expression to the left side
6x−x2−5−(8−2x)≥0
Subtract the terms
More Steps
Evaluate
6x−x2−5−(8−2x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
6x−x2−5−8+2x
Add the terms
More Steps
Evaluate
6x+2x
Collect like terms by calculating the sum or difference of their coefficients
(6+2)x
Add the numbers
8x
8x−x2−5−8
Subtract the numbers
8x−x2−13
8x−x2−13≥0
Rewrite the expression
8x−x2−13=0
Add or subtract both sides
8x−x2=13
Divide both sides
−18x−x2=−113
Evaluate
−8x+x2=−13
Add the same value to both sides
−8x+x2+16=−13+16
Simplify the expression
(x−4)2=3
Take the root of both sides of the equation and remember to use both positive and negative roots
x−4=±3
Separate the equation into 2 possible cases
x−4=3x−4=−3
Move the constant to the right-hand side and change its sign
x=3+4x−4=−3
Move the constant to the right-hand side and change its sign
x=3+4x=−3+4
Determine the test intervals using the critical values
x<−3+4−3+4<x<3+4x>3+4
Choose a value form each interval
x1=1x2=4x3=7
To determine if x<−3+4 is the solution to the inequality,test if the chosen value x=1 satisfies the initial inequality
More Steps
Evaluate
6×1−12−5≥8−2×1
Simplify
More Steps
Evaluate
6×1−12−5
1 raised to any power equals to 1
6×1−1−5
Any expression multiplied by 1 remains the same
6−1−5
Subtract the numbers
0
0≥8−2×1
Simplify
More Steps
Evaluate
8−2×1
Any expression multiplied by 1 remains the same
8−2
Subtract the numbers
6
0≥6
Check the inequality
false
x<−3+4 is not a solutionx2=4x3=7
To determine if −3+4<x<3+4 is the solution to the inequality,test if the chosen value x=4 satisfies the initial inequality
More Steps
Evaluate
6×4−42−5≥8−2×4
Simplify
More Steps
Evaluate
6×4−42−5
Multiply the numbers
24−42−5
Evaluate the power
24−16−5
Subtract the numbers
3
3≥8−2×4
Simplify
More Steps
Evaluate
8−2×4
Multiply the numbers
8−8
Subtract the terms
0
3≥0
Check the inequality
true
x<−3+4 is not a solution−3+4<x<3+4 is the solutionx3=7
To determine if x>3+4 is the solution to the inequality,test if the chosen value x=7 satisfies the initial inequality
More Steps
Evaluate
6×7−72−5≥8−2×7
Simplify
More Steps
Evaluate
6×7−72−5
Multiply the numbers
42−72−5
Evaluate the power
42−49−5
Subtract the numbers
−12
−12≥8−2×7
Simplify
More Steps
Evaluate
8−2×7
Multiply the numbers
8−14
Subtract the numbers
−6
−12≥−6
Check the inequality
false
x<−3+4 is not a solution−3+4<x<3+4 is the solutionx>3+4 is not a solution
The original inequality is a nonstrict inequality,so include the critical value in the solution
−3+4≤x≤3+4 is the solution
Solution
−3+4≤x≤3+4
Alternative Form
x∈[−3+4,3+4]
Show Solution
