Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈[−1,−3+1)∪(3+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 intersection
−1≤x≤3
Check if the solution is in the defined range
−1≤x≤3,x∈(−∞,−3+1)∪(3+1,+∞)
Solution
x∈[−1,−3+1)∪(3+1,3]
Show Solution
