Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
a>0
Alternative Form
a∈(0,+∞)
Evaluate
−373a−a<0
Find the domain
More Steps
Evaluate
73a≥0
Rewrite the expression
a≥0
−373a−a<0,a≥0
Move the expression to the right side
−373a<a
Change the signs on both sides of the inequality and flip the inequality sign
373a>−a
Separate the inequality into 2 possible cases
373a>−a,−a≥0373a>−a,−a<0
Solve the inequality
More Steps
Solve the inequality
373a>−a
Square both sides of the inequality
657a>(−a)2
Determine the sign
657a>a2
Move the expression to the left side
657a−a2>0
Evaluate
a2−657a<0
Add the same value to both sides
a2−657a+46572<46572
Evaluate
(a−2657)2<46572
Take the 2-th root on both sides of the inequality
(a−2657)2<46572
Calculate
a−2657<2657
Separate the inequality into 2 possible cases
{a−2657<2657a−2657>−2657
Calculate
More Steps
Evaluate
a−2657<2657
Move the constant to the right side
a<2657+2657
Add the numbers
a<657
{a<657a−2657>−2657
Cancel equal terms on both sides of the expression
{a<657a>0
Find the intersection
0<a<657
0<a<657,−a≥0373a>−a,−a<0
Change the signs on both sides of the inequality and flip the inequality sign
0<a<657,a≤0373a>−a,−a<0
Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of a
0<a<657,a≤0a∈R,−a<0
Change the signs on both sides of the inequality and flip the inequality sign
0<a<657,a≤0a∈R,a>0
Find the intersection
a∈∅a∈R,a>0
Find the intersection
a∈∅a>0
Find the union
a>0
Check if the solution is in the defined range
a>0,a≥0
Solution
a>0
Alternative Form
a∈(0,+∞)
Show Solution
