Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x∈(−∞,−334]∪[54,+∞)∪{0}
Evaluate
−3x49≤4x≤5x2
Separate into two inequalities
{−3x4×9≤4x4x≤5x2
Solve the inequality
More Steps
Evaluate
−3x4×9≤4x
Multiply the terms
−27x4≤4x
Add or subtract both sides
−27x4−4x≤0
Factor the expression
−x(27x3+4)≤0
Divide both sides
x(27x3+4)≥0
Separate the inequality into 2 possible cases
{x≥027x3+4≥0{x≤027x3+4≤0
Solve the inequality
More Steps
Evaluate
27x3+4≥0
Move the constant to the right side
27x3≥−4
Divide both sides
2727x3≥27−4
Divide the numbers
x3≥27−4
Use b−a=−ba=−ba to rewrite the fraction
x3≥−274
Take the 3-th root on both sides of the equation
3x3≥3−274
Calculate
x≥3−274
Simplify the root
x≥−334
{x≥0x≥−334{x≤027x3+4≤0
Solve the inequality
More Steps
Evaluate
27x3+4≤0
Move the constant to the right side
27x3≤−4
Divide both sides
2727x3≤27−4
Divide the numbers
x3≤27−4
Use b−a=−ba=−ba to rewrite the fraction
x3≤−274
Take the 3-th root on both sides of the equation
3x3≤3−274
Calculate
x≤3−274
Simplify the root
x≤−334
{x≥0x≥−334{x≤0x≤−334
Find the intersection
x≥0{x≤0x≤−334
Find the intersection
x≥0x≤−334
Find the union
x∈(−∞,−334]∪[0,+∞)
{x∈(−∞,−334]∪[0,+∞)4x≤5x2
Solve the inequality
More Steps
Evaluate
4x≤5x2
Add or subtract both sides
4x−5x2≤0
Evaluate
x2−54x≥0
Add the same value to both sides
x2−54x+254≥254
Evaluate
(x−52)2≥254
Take the 2-th root on both sides of the inequality
(x−52)2≥254
Calculate
x−52≥52
Separate the inequality into 2 possible cases
x−52≥52x−52≤−52
Calculate
More Steps
Evaluate
x−52≥52
Move the constant to the right side
x≥52+52
Add the numbers
x≥54
x≥54x−52≤−52
Cancel equal terms on both sides of the expression
x≥54x≤0
Find the union
x∈(−∞,0]∪[54,+∞)
{x∈(−∞,−334]∪[0,+∞)x∈(−∞,0]∪[54,+∞)
Solution
x∈(−∞,−334]∪[54,+∞)∪{0}
Show Solution
