Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
a∈(−∞,−1]∪{0}
Evaluate
−−(a×1)−a≥0
Find the domain
More Steps
Evaluate
−(a×1)≥0
Any expression multiplied by 1 remains the same
−a≥0
Change the signs on both sides of the inequality and flip the inequality sign
a≤0
−−(a×1)−a≥0,a≤0
Any expression multiplied by 1 remains the same
−−a−a≥0
Change the signs on both sides of the inequality and flip the inequality sign
−a+a≤0
Move the expression to the right side
−a≤−a
Separate the inequality into 2 possible cases
−a≤−a,−a≥0−a≤−a,−a<0
Solve the inequality
More Steps
Solve the inequality
−a≤−a
Square both sides of the inequality
−a≤(−a)2
Determine the sign
−a≤a2
Move the expression to the left side
−a−a2≤0
Evaluate
a2+a≥0
Add the same value to both sides
a2+a+41≥41
Evaluate
(a+21)2≥41
Take the 2-th root on both sides of the inequality
(a+21)2≥41
Calculate
a+21≥21
Separate the inequality into 2 possible cases
a+21≥21a+21≤−21
Cancel equal terms on both sides of the expression
a≥0a+21≤−21
Calculate
More Steps
Evaluate
a+21≤−21
Move the constant to the right side
a≤−21−21
Subtract the numbers
a≤−1
a≥0a≤−1
Find the union
a∈(−∞,−1]∪[0,+∞)
a∈(−∞,−1]∪[0,+∞),−a≥0−a≤−a,−a<0
Change the signs on both sides of the inequality and flip the inequality sign
a∈(−∞,−1]∪[0,+∞),a≤0−a≤−a,−a<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of a
a∈(−∞,−1]∪[0,+∞),a≤0a∈∅,−a<0
Change the signs on both sides of the inequality and flip the inequality sign
a∈(−∞,−1]∪[0,+∞),a≤0a∈∅,a>0
Find the intersection
a∈(−∞,−1]∪{0}a∈∅,a>0
Find the intersection
a∈(−∞,−1]∪{0}a∈∅
Find the union
a∈(−∞,−1]∪{0}
Check if the solution is in the defined range
a∈(−∞,−1]∪{0},a≤0
Solution
a∈(−∞,−1]∪{0}
Show Solution
