Problem 82 - Algebra 1

Question

Evaluate the expression for the given value of the variable. $$\text {m-5 when m=17}$$

Step-by-Step Solution

Answer

The evaluated result for the given value of the variable is 12.

Step 1: Identifying the given values

First, identify what values are given. In this case, the variable \(m\) is given the value 17.

Step 2: Substitute the given value

The next step is substituting the given \(m\) value into the equation. This results in \(17 - 5\).

Step 3: Performing the operation

The last step is to perform the operation of subtraction which results in 12

Key Concepts

Variable Substitution

Variable substitution is an essential technique in algebra that helps simplify expressions and solve equations. It involves replacing a variable in an expression with a given numerical value. This is particularly useful when the goal is to evaluate an expression for specific variable values. In the given exercise, the variable \( m \) has been assigned the value 17.

• Start by identifying the variable within the expression. In this case, it is \( m \).
• Find the corresponding numerical value for \( m \), which is 17.
• Substitute the value 17 in place of \( m \) within the expression, transforming \( m - 5 \) into \( 17 - 5 \).

This process allows us to transform an abstract expression with variables into a straightforward numerical calculation. It simplifies solving by removing the variables entirely in favor of given numbers.

Basic Arithmetic

Basic arithmetic refers to the foundational mathematical operations, including addition, subtraction, multiplication, and division. For this exercise, the focus is specifically on subtraction.
Subtraction is the process of deducting a number from another, effectively decreasing its value. In algebraic expression contexts, once variable substitution has been completed, the next step often involves performing subtraction.

• The expression \( 17 - 5 \) means starting with the number 17 and subtracting 5 from it.
• Subtracting 5 from 17 decreases the initial value, resulting in 12.

Practicing basic arithmetic ensures stronger math skills and helps in solving more complex algebraic expressions. Always take note of the order of operations, though in simple expressions like this, subtraction is straightforward.

Mathematical Operations

Mathematical operations are at the core of manipulating and solving equations and algebraic expressions. These operations, including addition, subtraction, multiplication, and division, allow us to evaluate and simplify expressions after variable substitution.
In the exercise provided, the primary operation used is subtraction. After substituting 17 for the variable \( m \), what remains is a basic arithmetic operation: subtracting 5 from 17. It’s important to clearly perform this operation step-by-step:

• Write out the substituted expression: \( 17 - 5 \).
• Carefully perform the subtraction, making sure each step is correct. Compute \( 17 - 5 \) to reach the final solution, which is 12.

Understanding and practicing mathematical operations is crucial, as these are the building blocks to tackling more advanced algebra problems. Begin with fundamental operations for a solid mathematical foundation.