Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−1]∪[3,+∞)
Evaluate
log10(x2−2x−2)≥0
Find the domain
More Steps
Evaluate
x2−2x−2>0
Move the constant to the right side
x2−2x>0−(−2)
Add the terms
x2−2x>2
Add the same value to both sides
x2−2x+1>2+1
Evaluate
x2−2x+1>3
Evaluate
(x−1)2>3
Take the 2-th root on both sides of the inequality
(x−1)2>3
Calculate
∣x−1∣>3
Separate the inequality into 2 possible cases
x−1>3x−1<−3
Calculate
x>3+1x−1<−3
Calculate
x>3+1x<−3+1
Find the union
x∈(−∞,−3+1)∪(3+1,+∞)
log10(x2−2x−2)≥0,x∈(−∞,−3+1)∪(3+1,+∞)
For 10>1 the expression log10(x2−2x−2)≥0 is equivalent to x2−2x−2≥100
x2−2x−2≥100
Evaluate the power
x2−2x−2≥1
Move the expression to the left side
x2−2x−2−1≥0
Subtract the numbers
x2−2x−3≥0
Move the constant to the right side
x2−2x≥0−(−3)
Add the terms
x2−2x≥3
Add the same value to both sides
x2−2x+1≥3+1
Evaluate
x2−2x+1≥4
Evaluate
(x−1)2≥4
Take the 2-th root on both sides of the inequality
(x−1)2≥4
Calculate
∣x−1∣≥2
Separate the inequality into 2 possible cases
x−1≥2x−1≤−2
Calculate
More Steps
Evaluate
x−1≥2
Move the constant to the right side
x≥2+1
Add the numbers
x≥3
x≥3x−1≤−2
Calculate
More Steps
Evaluate
x−1≤−2
Move the constant to the right side
x≤−2+1
Add the numbers
x≤−1
x≥3x≤−1
Find the union
x∈(−∞,−1]∪[3,+∞)
Check if the solution is in the defined range
x∈(−∞,−1]∪[3,+∞),x∈(−∞,−3+1)∪(3+1,+∞)
Solution
x∈(−∞,−1]∪[3,+∞)
Show Solution
