Problem 38 - Prealgebra

Question

Evaluate each expression if \(m=8\) and \(y=6\). $$(2 m+3 y)-m$$

Step-by-Step Solution

Answer

The value of the expression is 26.

Step 1: Substitute Values

In this expression, substitute the given values of \(m = 8\) and \(y = 6\) into the expression \((2m + 3y) - m\). This gives us \((2(8) + 3(6)) - 8\).

Step 2: Simplify Operations in Parentheses

First, perform the multiplication within the parentheses: \( 2(8) = 16\) and \( 3(6) = 18\). Now, substitute these values back into the expression to get \((16 + 18) - 8\).

Step 3: Evaluate the Expression in Parentheses

Add the numbers within the parentheses: \(16 + 18 = 34\). The expression now simplifies to \(34 - 8\).

Step 4: Final Calculation

Subtract the value \(m = 8\) from 34: \(34 - 8 = 26\).

Key Concepts

Variable Substitution

When tackling expressions such as \((2m + 3y) - m\), the first step is to replace variables with their given numerical values. This process is known as variable substitution. In our example, we know the values of the variables: \(m = 8\) and \(y = 6\). Hence, when we perform variable substitution, it involves plugging these values into the expression. Instead of dealing with letters, we now have numbers: \((2(8) + 3(6)) - 8\). Anything in math becomes much clearer when it's numerical, making it easier to carry out the calculations and simplifies the task at hand.

Evaluating Expressions

Following variable substitution, the next step is to evaluate the expression. Evaluating refers to performing the arithmetic operations as per the given expression.

The expression from the previous step becomes \((2(8) + 3(6)) - 8\). Here's how we evaluate it:

• First, perform the operations within the parentheses. This includes multiplying \(2\) and \(8\), which results in \(16\), and multiplying \(3\) and \(6\), resulting in \(18\).
• After obtaining the results of these multiplications, the expression within the parentheses now reads \(16 + 18\).

Evaluating means calculating step-by-step to ensure no mathematical details are missed. This methodical approach is crucial to solve expressions accurately.

Simplifying Expressions

Once we have evaluated the basic mathematical operations, it's time to simplify the expression. Simplification makes the expression easier to understand and manage.

Consider the evaluated parts of our expression: \((16 + 18) - 8\). The next step is to simplify it by solving the operations:

• Add \(16\) and \(18\) to get \(34\).
• Lastly, subtract \(8\) from \(34\), which simplifies the expression to \(26\).

Simplification is the process of reducing an expression to its most basic form, making it more concise and straightforward to work with. It's like tidying up a room by putting everything in its place!