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loraboiago
- 3
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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 said: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 said: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 said: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.
Algebraic expressions are mathematical statements that contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to represent relationships between quantities and can be evaluated to obtain a numerical value.
To simplify an algebraic expression, you need to combine like terms by combining the coefficients of the same variables. Then, you can use the distributive property to remove parentheses and combine any remaining like terms. Finally, you can simplify any exponents or perform any necessary operations to obtain the simplest form of the expression.
Yes, there are several rules that can be followed to simplify algebraic expressions. These include the commutative, associative, and distributive properties, as well as rules for combining like terms and simplifying exponents. It is important to follow these rules carefully to ensure that the expression is simplified correctly.
Simplifying algebraic expressions can make them easier to work with and understand. It can also help in solving equations and problems involving these expressions. In addition, simplifying can help to identify patterns and relationships between quantities, making it easier to interpret and apply the expression in real-world situations.
Yes, there are often multiple ways to simplify an algebraic expression. It is important to follow the rules for simplifying and to choose the most efficient method for the specific expression. It is also important to check the final simplification to ensure that it is equivalent to the original expression.