Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
a≥0
Alternative Form
a∈[0,+∞)
Evaluate
−3−73a−a<0
Find the domain
More Steps
Evaluate
73a≥0
Rewrite the expression
a≥0
−3−73a−a<0,a≥0
Change the signs on both sides of the inequality and flip the inequality sign
73a+3+a>0
Move the expression to the right side
73a>−3−a
Separate the inequality into 2 possible cases
73a>−3−a,−3−a≥073a>−3−a,−3−a<0
Solve the inequality
More Steps
Solve the inequality
73a>−3−a
Square both sides of the inequality
73a>(−3−a)2
Expand the expression
73a>9+6a+a2
Move the expression to the left side
73a−(9+6a+a2)>0
Subtract the terms
More Steps
Evaluate
73a−(9+6a+a2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
73a−9−6a−a2
Subtract the terms
67a−9−a2
67a−9−a2>0
Move the constant to the right side
67a−a2>0−(−9)
Add the terms
67a−a2>9
Evaluate
a2−67a<−9
Add the same value to both sides
a2−67a+44489<−9+44489
Evaluate
a2−67a+44489<44453
Evaluate
(a−267)2<44453
Take the 2-th root on both sides of the inequality
(a−267)2<44453
Calculate
a−267<24453
Separate the inequality into 2 possible cases
{a−267<24453a−267>−24453
Calculate
More Steps
Evaluate
a−267<24453
Move the constant to the right side
a<24453+267
Write all numerators above the common denominator
a<24453+67
{a<24453+67a−267>−24453
Calculate
More Steps
Evaluate
a−267>−24453
Move the constant to the right side
a>−24453+267
Write all numerators above the common denominator
a>2−4453+67
{a<24453+67a>2−4453+67
Find the intersection
2−4453+67<a<24453+67
2−4453+67<a<24453+67,−3−a≥073a>−3−a,−3−a<0
Solve the inequality
More Steps
Evaluate
−3−a≥0
Move the constant to the right side
−a≥0+3
Removing 0 doesn't change the value,so remove it from the expression
−a≥3
Change the signs on both sides of the inequality and flip the inequality sign
a≤−3
2−4453+67<a<24453+67,a≤−373a>−3−a,−3−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
2−4453+67<a<24453+67,a≤−3a∈R,−3−a<0
Solve the inequality
More Steps
Evaluate
−3−a<0
Move the constant to the right side
−a<0+3
Removing 0 doesn't change the value,so remove it from the expression
−a<3
Change the signs on both sides of the inequality and flip the inequality sign
a>−3
2−4453+67<a<24453+67,a≤−3a∈R,a>−3
Find the intersection
a∈∅a∈R,a>−3
Find the intersection
a∈∅a>−3
Find the union
a>−3
Check if the solution is in the defined range
a>−3,a≥0
Solution
a≥0
Alternative Form
a∈[0,+∞)
Show Solution
