Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve for y
y∈∅
Alternative Form
No solution
Evaluate
−3(y−4)<−5y2
Move the expression to the left side
−3(y−4)−(−5y2)<0
Subtract the terms
More Steps
Evaluate
−3(y−4)−(−5y2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−3(y−4)+5y2
Expand the expression
More Steps
Calculate
−3(y−4)
Apply the distributive property
−3y−(−3×4)
Multiply the numbers
−3y−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−3y+12
−3y+12+5y2
−3y+12+5y2<0
Rewrite the expression
−3y+12+5y2=0
Add or subtract both sides
−3y+5y2=−12
Divide both sides
5−3y+5y2=5−12
Evaluate
−53y+y2=−512
Add the same value to both sides
−53y+y2+1009=−512+1009
Simplify the expression
(y−103)2=−100231
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 y
y∈/R
There are no key numbers,so choose any value to test,for example y=0
y=0
Solution
More Steps
Evaluate
−3(0−4)<−5×02
Simplify
More Steps
Evaluate
−3(0−4)
Removing 0 doesn't change the value,so remove it from the expression
−3(−4)
Multiplying or dividing an even number of negative terms equals a positive
3×4
Multiply the numbers
12
12<−5×02
Simplify
More Steps
Evaluate
−5×02
Calculate
−5×0
Any expression multiplied by 0 equals 0
0
12<0
Check the inequality
false
y∈∅
Alternative Form
No solution
Show Solution
