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In algebra, simplifying expressions is a core skill you need to master. When you encounter an expression like \(-3m - 5m\), the goal is to make it as simple as possible. Here, you can simplify by combining the terms together because they both contain the variable \(m\). Start by adding both coefficients: - The coefficient of \(m\) in \(-3m\) is \(-3\). - The coefficient of \(m\) in \(-5m\) is \(-5\). When you add these two coefficients, you will get \(-8\). Therefore, the expression \(-3m - 5m\) can be rewritten as \(-8m\).
Simplifying algebraic expressions involves reducing them to their simplest form while maintaining equality. This makes equations easier to manage and solutions more straightforward. Always look for common terms and simplify by performing operations among them.

Combining like terms is another foundational technique in algebra. Like terms are terms that have the same variables raised to the same power. In the equation \(-3m - 5m = \frac{4}{7}\), the terms \(-3m\) and \(-5m\) are like terms because they both contain the variable \(m\).
To combine like terms, you perform operations on their coefficients. For \(-3m\) and \(-5m\), we add their coefficients:

• Add: \(-3 + (-5) = -8\)

This reduces the terms into one, making your equation simpler \(-8m = \frac{4}{7}\).
Combining like terms not only simplifies the expression but also helps in finding a clearer path to the solution. This step is crucial before any further moves, like isolating variables or performing operations, especially in equations.

Once you've simplified your equation by combining like terms, you may need to perform division to isolate the variable and solve the equation. In our example equation \(-8m = \frac{4}{7}\), the variable \(m\) can be isolated by dividing both sides of the equation by \(-8\).
When you divide by a negative number, it’s essential to maintain the balance of the equation. Here’s how it's done:

• Divide both sides: \(m = \frac{4}{7} \div (-8)\)
• This is equivalent to multiplying: \(m = \frac{4}{7} \times \frac{1}{-8}\)

In algebra, dividing by a number is the same as multiplying by its reciprocal. Simplifying results in \(m = \frac{4}{-56}\), which further reduces to \(-\frac{1}{14}\).
Mastering division in equations is vital for solving algebraic equations efficiently. It helps isolate variables, making the equation simpler to navigate and solve correctly. It is crucial to remember to adjust the signs properly to avoid errors in the solution.