Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x=23
Alternative Form
x=1.5
Evaluate
18x=12xx>0
Separate into two inequalities
{18x=12x×x12x×x>0
Solve the inequality
More Steps
Evaluate
18x=12x×x
Multiply the terms
18x=12x2
Add or subtract both sides
18x−12x2=0
Factor the expression
More Steps
Evaluate
18x−12x2
Rewrite the expression
6x×3−6x×2x
Factor out 6x from the expression
6x(3−2x)
6x(3−2x)=0
When the product of factors equals 0,at least one factor is 0
6x=03−2x=0
Solve the equation for x
x=03−2x=0
Solve the equation for x
More Steps
Evaluate
3−2x=0
Move the constant to the right-hand side and change its sign
−2x=0−3
Removing 0 doesn't change the value,so remove it from the expression
−2x=−3
Change the signs on both sides of the equation
2x=3
Divide both sides
22x=23
Divide the numbers
x=23
x=0x=23
Calculate
x=0∪x=23
{x=0∪x=2312x×x>0
Solve the inequality
More Steps
Evaluate
12x×x>0
Multiply the terms
12x2>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when 12x2=0
12x2=0
Rewrite the expression
x2=0
The only way a power can be 0 is when the base equals 0
x=0
Exclude the impossible values of x
x=0
{x=0∪x=23x=0
Find the intersection
x=23
Solution
More Steps
Check the solution
{18×23=12×23×2312×23×23>0
Simplify
{27=2712×1.5×1.5>0
Evaluate
true
x=23
Alternative Form
x=1.5
Show Solution
