Problem 48 - Elementary Algebra

Question

\(-6(5 v)\)

Step-by-Step Solution

Answer

-30v

Step 1: Understand the Expression

The given expression is \(-6(5v)\). This is a multiplication problem where you need to multiply \(-6\) and \(5v\).

Step 2: Multiply the Constants

First, multiply the numerical coefficients (constants) \(-6\) and \(5\). To do this, multiply \(-6 \times 5\).

Step 3: Calculate the Product

Calculate \(-6 \times 5 = -30\). So, the product of the constants is \(-30\).

Step 4: Include the Variable

Attach the variable \(v\) to the product you obtained in the previous step. Thus, the solution is \(-30v\).

Step 5: Final Answer

The simplified form of the expression \(-6(5v)\) is \-30v\.

Key Concepts

multiplication of constants

When multiplying expressions, you often start with the numerical parts, called 'constants.'
These are the actual numbers without any variables.
For example, in \(-6(5v)\), \(-6\) and \(5\) are constants.
When multiplying constants, follow the standard multiplication rules you learned in primary school.
Here, \(-6 \times 5 = -30\).
Remember, multiplying a negative number by a positive number always gives a negative result.
So always pay attention to the signs of the numbers you are multiplying.

working with variables

Variables are symbols (like \(v\)) that represent numbers in algebraic expressions.
They are used to denote unknown values or quantities that can change.
When multiplying constants and variables, always start with the constants.
In the expression \(-6(5v)\), you first multiply the constants \(-6\) and \(5\).
Then, attach the variable to the product of these constants.
So, \(-30 \times v\) becomes \(-30v\).
This means you scaled the variable \(v\) by the product of the constants.

simplifying expressions

Simplifying expressions means combining and reducing them to their most basic form.
This typically involves:

• Multiplying constants
• Attaching variables

Start by simplifying any constants you need to multiply.
Then, ensure all like terms are combined.
In our example \(-6(5v)\), you first multiply \(-6 \times 5 = -30\).
Then, you attach the variable \(v\), leading to \(-30v\).
That is the simplified form of the original expression.
Always double-check your work to make sure all steps are followed and to avoid mistakes.