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Algebraic Expressions Simplified

loraboiago

New member
Nov 29, 2013
3
How does 3x or (x-5) equal 0 in the statement 3x(x-5)=0? I don't understand the logic behind it. Thank you!!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
If you have the statement:

\(\displaystyle a\cdot b=0\) where \(\displaystyle a\ne b\)

Then the only way it can be true is if either \(\displaystyle a=0\) or \(\displaystyle b=0\). This is called the zero-factor property.
 

loraboiago

New member
Nov 29, 2013
3
If you have the statement:

\(\displaystyle a\cdot b=0\) where \(\displaystyle a\ne b\)

Then the only way it can be true is if either \(\displaystyle a=0\) or \(\displaystyle b=0\). This is called the zero-factor property.
Thank you Mark for the quick and helpful response. The answer to this question went on to explain "3x(x-5)=0 provides an equation in which at least one of the expressions 3x or (x-5) is equal to 0. That translates into two possible values for x: 0 and 5."

I understand how one can equal 0 (thanks to you!), but how do I calculate the other possible value as being 5?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Thank you Mark for the quick and helpful response. The answer to this question went on to explain "3x(x-5)=0 provides an equation in which at least one of the expressions 3x or (x-5) is equal to 0. That translates into two possible values for x: 0 and 5."

I understand how one can equal 0 (thanks to you!), but how do I calculate the other possible value as being 5?
I would look at it as 3 factors being equal to zero:

\(\displaystyle 3\cdot x\cdot(x-5)=0\)

Now, set all factors involving $x$ equal to zero, and then solve for $x$ in each equation:

\(\displaystyle x=0\)

\(\displaystyle x-5=0\)

The solutions to these equations will give you the solutions to the original equation.
 

loraboiago

New member
Nov 29, 2013
3
I would look at it as 3 factors being equal to zero:

\(\displaystyle 3\cdot x\cdot(x-5)=0\)

Now, set all factors involving $x$ equal to zero, and then solve for $x$ in each equation:

\(\displaystyle x=0\)

\(\displaystyle x-5=0\)

The solutions to these equations will give you the solutions to the original equation.
Ah got it! You are awesome. Thank you :)