Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−4]∪[6,+∞)
Evaluate
52∣x−1∣≥2
Multiply both sides of the inequality by 5
52∣x−1∣×5≥2×5
Multiply the terms
2∣x−1∣≥2×5
Multiply the terms
2∣x−1∣≥10
Divide both sides
22∣x−1∣≥210
Divide the numbers
∣x−1∣≥210
Divide the numbers
More Steps
Evaluate
210
Reduce the numbers
15
Calculate
5
∣x−1∣≥5
Separate the inequality into 2 possible cases
x−1≥5x−1≤−5
Solve the inequality for x
More Steps
Evaluate
x−1≥5
Move the constant to the right side
x≥5+1
Add the numbers
x≥6
x≥6x−1≤−5
Solve the inequality for x
More Steps
Evaluate
x−1≤−5
Move the constant to the right side
x≤−5+1
Add the numbers
x≤−4
x≥6x≤−4
Solution
x∈(−∞,−4]∪[6,+∞)
Show Solution
