Mastering the Constant Multiple Rule: Simplify Expressions and Solve Equations with Ease!

Constant Multiple Rule

The Constant Multiple Rule is a rule in mathematics that allows us to simplify expressions involving a constant and a variable

The Constant Multiple Rule is a rule in mathematics that allows us to simplify expressions involving a constant and a variable. It states that if we have a constant multiplied by a variable, we can factor out the constant and multiply it separately.

Formally, if “a” is a constant and “x” is a variable, then “a * x” can be rewritten as “a” multiplied by “x”.

For example, let’s say we have the expression 4x. Using the Constant Multiple Rule, we can rewrite this as 4 * x. This means that the constant 4 is multiplied by the variable x.

Similarly, let’s say we have the expression -2y. Using the Constant Multiple Rule, we can rewrite this as -2 * y. Here, the constant -2 is multiplied by the variable y.

The Constant Multiple Rule is particularly useful when we need to simplify algebraic expressions or solve equations. It allows us to separate the constant and the variable, making calculations and operations easier.

Here are a few examples of how the Constant Multiple Rule can be applied:

1. Simplify the expression 3a – 2a + 4a:
Here, we can factor out the coefficients (constants) of the variables, using the Constant Multiple Rule.
3a – 2a + 4a = (3 – 2 + 4) * a = 5a

2. Solve the equation 2x = 10:
We want to isolate the variable x. Using the Constant Multiple Rule, we can divide both sides of the equation by the coefficient of x.
2x / 2 = 10 / 2
x = 5

In summary, the Constant Multiple Rule allows us to simplify expressions and solve equations by factoring out the constant and multiplying it separately with the variable. It is a helpful tool in algebraic manipulations and calculations involving constants and variables.

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