Question
Solve the inequality
−32≤x≤32
Alternative Form
x∈[−32,32]
Evaluate
−1≤21x2x≤1
Separate into two inequalities
{−1≤21×x2x21×x2x≤1
Solve the inequality
More Steps

Evaluate
−1≤21×x2x
Simplify
More Steps

Evaluate
21×x2x
Any expression multiplied by 1 remains the same
2x2x
Multiply the terms
2x2×x
Multiply the terms
2x3
−1≤2x3
Swap the sides of the inequality
2x3≥−1
Cross multiply
x3≥2(−1)
Simplify the equation
x3≥−2
Take the 3-th root on both sides of the equation
3x3≥3−2
Calculate
x≥3−2
An odd root of a negative radicand is always a negative
x≥−32
{x≥−3221×x2x≤1
Solve the inequality
More Steps

Evaluate
21×x2x≤1
Simplify
More Steps

Evaluate
21×x2x
Any expression multiplied by 1 remains the same
2x2x
Multiply the terms
2x2×x
Multiply the terms
2x3
2x3≤1
Cross multiply
x3≤2
Take the 3-th root on both sides of the equation
3x3≤32
Calculate
x≤32
{x≥−32x≤32
Solution
−32≤x≤32
Alternative Form
x∈[−32,32]
Show Solution
