Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈[−27,1]∪[2,213]
Evaluate
1≤∣2x−3∣≤10
Separate into two inequalities
{1≤∣2x−3∣∣2x−3∣≤10
Solve the inequality
More Steps
Evaluate
1≤∣2x−3∣
Swap the sides of the inequality
∣2x−3∣≥1
Separate the inequality into 2 possible cases
2x−3≥12x−3≤−1
Solve the inequality for x
More Steps
Evaluate
2x−3≥1
Move the constant to the right side
2x≥1+3
Add the numbers
2x≥4
Divide both sides
22x≥24
Divide the numbers
x≥24
Divide the numbers
x≥2
x≥22x−3≤−1
Solve the inequality for x
More Steps
Evaluate
2x−3≤−1
Move the constant to the right side
2x≤−1+3
Add the numbers
2x≤2
Divide both sides
22x≤22
Divide the numbers
x≤22
Divide the numbers
x≤1
x≥2x≤1
Find the union
x∈(−∞,1]∪[2,+∞)
{x∈(−∞,1]∪[2,+∞)∣2x−3∣≤10
Solve the inequality
More Steps
Evaluate
∣2x−3∣≤10
Separate the inequality into 2 possible cases
{2x−3≤102x−3≥−10
Solve the inequality for x
More Steps
Evaluate
2x−3≤10
Move the constant to the right side
2x≤10+3
Add the numbers
2x≤13
Divide both sides
22x≤213
Divide the numbers
x≤213
{x≤2132x−3≥−10
Solve the inequality for x
More Steps
Evaluate
2x−3≥−10
Move the constant to the right side
2x≥−10+3
Add the numbers
2x≥−7
Divide both sides
22x≥2−7
Divide the numbers
x≥2−7
Use b−a=−ba=−ba to rewrite the fraction
x≥−27
{x≤213x≥−27
Find the intersection
−27≤x≤213
{x∈(−∞,1]∪[2,+∞)−27≤x≤213
Solution
x∈[−27,1]∪[2,213]
Show Solution
