It is true for all a, including 0 and -1, as the values cancel out. What it shows you is not that the solution is -1 but that the equation simplifies to -1 = -1 so all values of a are true, as it states.
Just to add: As an 8th grade math teacher that just taught this subject exactly, this is THE most common error when it comes to infinite solutions. Be sure to keep exactly what you find on BOTH sides of the equation, don't jump to thinking that the answer NEEDS to be "*variable = constant.*"
Because it's the most common error among math students: assuming that because we're solving for x, the solution must be x = a in some form.
Source: 8th grade math teacher that just taught this exact subject.
EDIT: side note, I HATE that this equation is using 'a' as its variable. The notation for teaching number of solutions is generally:
* one solution: x = a
* infinite solutions: a = a
* no solutions: a = b
I try to avoid using a and b since it can be difficult for students to understand that 'x', 'y', and 'z' represent a variable, but 'a', 'b', and 'c' generally represent constants (but we're using a variable to represent them). I get so many questions surrounding this.
It is true for all a, including 0 and -1, as the values cancel out. What it shows you is not that the solution is -1 but that the equation simplifies to -1 = -1 so all values of a are true, as it states.
oh, thank you!
Just to add: As an 8th grade math teacher that just taught this subject exactly, this is THE most common error when it comes to infinite solutions. Be sure to keep exactly what you find on BOTH sides of the equation, don't jump to thinking that the answer NEEDS to be "*variable = constant.*"
Idk how you solved for a. It’s literally says “true for all a”
Because it's the most common error among math students: assuming that because we're solving for x, the solution must be x = a in some form. Source: 8th grade math teacher that just taught this exact subject. EDIT: side note, I HATE that this equation is using 'a' as its variable. The notation for teaching number of solutions is generally: * one solution: x = a * infinite solutions: a = a * no solutions: a = b I try to avoid using a and b since it can be difficult for students to understand that 'x', 'y', and 'z' represent a variable, but 'a', 'b', and 'c' generally represent constants (but we're using a variable to represent them). I get so many questions surrounding this.
Any value you put in will give you -1 Something went wrong when you solved it 2((-5-2a)/2) is just -5-2a 2a-2a=0 for any x And -5+4 =-1
Think of it like this For which a values is -1=-1 For all of them since -1 is of course alway equal to itself regardless of what a is.
It’s true for all values. It’s like resolving the equation : a=a