Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
p>1
Alternative Form
p∈(1,+∞)
Evaluate
p>p
Find the domain
p>p,p≥0
Swap the sides
p<p
Separate the inequality into 2 possible cases
p<p,p≥0p<p,p<0
Solve the inequality
More Steps
Solve the inequality
p<p
Square both sides of the inequality
p<p2
Move the expression to the left side
p−p2<0
Evaluate
p2−p>0
Add the same value to both sides
p2−p+41>41
Evaluate
(p−21)2>41
Take the 2-th root on both sides of the inequality
(p−21)2>41
Calculate
p−21>21
Separate the inequality into 2 possible cases
p−21>21p−21<−21
Calculate
More Steps
Evaluate
p−21>21
Move the constant to the right side
p>21+21
Add the numbers
p>1
p>1p−21<−21
Cancel equal terms on both sides of the expression
p>1p<0
Find the union
p∈(−∞,0)∪(1,+∞)
p∈(−∞,0)∪(1,+∞),p≥0p<p,p<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 p
p∈(−∞,0)∪(1,+∞),p≥0p∈∅,p<0
Find the intersection
p>1p∈∅,p<0
Find the intersection
p>1p∈∅
Find the union
p>1
Check if the solution is in the defined range
p>1,p≥0
Solution
p>1
Alternative Form
p∈(1,+∞)
Show Solution
