Problem 63 - Algebra A Combined Function

Question

Perform each indicated operation. Don't forget to simplify if possible. Subtract \(5 m-6\) from \(m-9\)

Step-by-Step Solution

Answer

The result is \(-4m - 3\).

Step 1: Understand the Problem

We are asked to subtract two expressions. Specifically, we need to subtract the expression \(5m - 6\) from the expression \(m - 9\). In mathematical terms, this means we need to calculate \((m - 9) - (5m - 6)\).

Step 2: Distribute the Negative Sign

When subtracting, we distribute the negative sign across the second expression. This means we change the signs of each term in \(5m - 6\) to get \(-5m + 6\). Now our expression is \(m - 9 - 5m + 6\).

Step 3: Combine Like Terms

Now, we combine like terms. First, combine the \(m\) terms: \(m - 5m = -4m\). Next, combine the constant terms: \(-9 + 6 = -3\). Thus, the expression simplifies to \(-4m - 3\).

Step 4: Simplify the Expression

Ensure that the expression \(-4m - 3\) cannot be simplified further. There are no like terms to combine, so this is the final simplified form.

Key Concepts

Simplifying Expressions

Simplifying expressions in algebra involves reducing them to their most concise form while keeping the same value. The goal is to make the expression easier to work with—say goodbye to unnecessary complexity! In our example, we start with the expression \(m - 9 - 5m + 6\).

• First, identify any like terms in the expression, which are terms that have the same variable components.
• Make sure to carry out basic arithmetic between those terms to simplify.

Remember, simplifying doesn't change the expression's value but translates it into a cleaner form. The expression \(-4m - 3\) is already in its simplest form as there are no more like terms left to combine.

Subtraction of Expressions

Subtraction in algebra can be thought of as adding a negative. When you subtract one expression from another, like \((m - 9) - (5m - 6)\), this involves changing the signs of every term in the second expression.

• Write the expression you are subtracting from first, without any change.
• Distribute the subtraction or minus sign across the terms inside the parentheses of the second expression.
• In our case, we take \(5m - 6\) and change it to \(-5m + 6\) \(\).

Simplifies the problem by effectively turning it into an addition of two terms, one of which has been negated. This method helps prevent sign errors and ensures accurate computation.

Combining Like Terms

Combining like terms is an essential concept when working with algebraic expressions. Like terms are terms that contain the same variables raised to the same power. In our example, the terms \(m\) and \(5m\) are like terms.

• First, identify these terms within your expression.
• Add or subtract their coefficients accordingly. For instance, \(m - 5m\) simplifies to \(-4m\).
• Similarly, the constants, such as \(-9\) and \(+6\), are also combined to yield \(-3\).

Combining like terms helps condense expressions and is a critical step to ensure that your final answer is simplified. By doing this, you lay the groundwork for solving more complex equations.