Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x≥221
Alternative Form
x∈[221,+∞)
Evaluate
∣x−1∣−3x×7≤0
Multiply the terms
∣x−1∣−21x≤0
Separate the inequality into 2 possible cases
x−1−21x≤0,x−1≥0−(x−1)−21x≤0,x−1<0
Evaluate
More Steps
Evaluate
x−1−21x≤0
Simplify the expression
−20x−1≤0
Move the constant to the right side
−20x≤0+1
Removing 0 doesn't change the value,so remove it from the expression
−20x≤1
Change the signs on both sides of the inequality and flip the inequality sign
20x≥−1
Divide both sides
2020x≥20−1
Divide the numbers
x≥20−1
Use b−a=−ba=−ba to rewrite the fraction
x≥−201
x≥−201,x−1≥0−(x−1)−21x≤0,x−1<0
Evaluate
More Steps
Evaluate
x−1≥0
Move the constant to the right side
x≥0+1
Removing 0 doesn't change the value,so remove it from the expression
x≥1
x≥−201,x≥1−(x−1)−21x≤0,x−1<0
Evaluate
More Steps
Evaluate
−(x−1)−21x≤0
Remove the parentheses
−x+1−21x≤0
Simplify the expression
−22x+1≤0
Move the constant to the right side
−22x≤0−1
Removing 0 doesn't change the value,so remove it from the expression
−22x≤−1
Change the signs on both sides of the inequality and flip the inequality sign
22x≥1
Divide both sides
2222x≥221
Divide the numbers
x≥221
x≥−201,x≥1x≥221,x−1<0
Evaluate
More Steps
Evaluate
x−1<0
Move the constant to the right side
x<0+1
Removing 0 doesn't change the value,so remove it from the expression
x<1
x≥−201,x≥1x≥221,x<1
Find the intersection
x≥1x≥221,x<1
Find the intersection
x≥1221≤x<1
Solution
x≥221
Alternative Form
x∈[221,+∞)
Show Solution
