Problem 22 - Algebra 1

Question

\(9+p\) when \(p=11\)

Step-by-Step Solution

Answer

The solution for \(9+p\) when \(p=11\) is \(20\).

Step 1: Identify the variable

The problem involves an algebraic expression \(9+p\). Here, \(p\) is the variable.

Step 2: Substitute the variable

It's provided that \(p=11\). Substitute this value into the expression to replace \(p\). This gives us \(9+11\).

Step 3: Perform the operation

Perform the addition operation. \(9+11\) equals \(20\).

Key Concepts

Understanding Variables in Algebra

In algebra, a variable is a symbol that represents an unknown or changeable number. These symbols, most commonly letters like \(p\), \(x\), or \(y\), allow us to create equations and expressions to describe a wide range of situations.
Variables can vary; their value is not fixed unless defined in a given problem. In the expression \(9+p\), \(p\) is the variable. It acts as a placeholder for a value that can be specified, like a container waiting to be filled.
Knowing what a variable is and how to recognize it is important in making sense of algebraic expressions and performing further operations on them.

The Role of Substitution

Substitution is a key skill in algebra. It involves replacing a variable with a specific value given in a problem. In our case, the problem gives \(p = 11\). Substitution helps turn an abstract expression into a concrete one, enabling us to solve it numerically.
To substitute, simply replace the variable with its value in the expression. For \(9+p\), substitute \(p\) with 11, transforming the expression to \(9+11\).

• Identify the variable in the expression.
• Replace it with the provided value.

This action simplifies the problem, making it ready for the next operation.

Basics of Addition in Algebra

Addition is one of the elementary operations used in algebra. It is the process of combining two numbers to get a sum. In our example, after substitution, we are left with \(9+11\).
Performing the addition involves combining these two numbers. Adding 11 to 9, we sum them to reach 20, which is a straightforward computation.
Understanding addition in algebra involves recognizing when and how to combine numbers. Some practical tips include:

• Always line up numbers by their place values when working out sums manually.
• Remember that addition is commutative: \(a + b = b + a\).

This simple yet crucial operation is foundational to moving forward with more complex algebraic procedures.