Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x=x-2
the equation has
one solution
infinite solutions
no solution
The equation x = x - 2 has no solution.
Let's solve the equation to confirm this:
x = x - 2
By subtracting x from both sides of the equation, we get:
0 = -2
This equation is inconsistent since 0 does not equal -2. Thus, the equation x = x - 2 has no solution.
Two values of x that support this conclusion are any two distinct real numbers. For example, x = 5 and x = 6. If you substitute these values into the equation, you will find that they do not make the equation true.
A value of x that makes the equation true is blank
, which when substituted into the equation and simplified makes the equation turn into
equals blank = blank
.A value of x that makes the equation false is blank
, which when substituted into the equation and simplified makes the equation turn into
equals blank = blank
.
A value of x that makes the equation true is not possible since the equation x = x - 2 has no solution.
A value of x that makes the equation false is also not possible since the equation x = x - 2 has no solution.
fill in the blanks
I apologize for the confusion in my previous response. Let's fill in the blanks correctly:
A value of x that makes the equation true is not possible since the equation x = x - 2 has no solution.
A value of x that makes the equation false is not applicable since the equation x = x - 2 has no solution.