Problem 94 - Elementary and Intermediate Algebra

Question

Simplify each expression, if possible. $$ -5.7 m+4.3 m $$

Step-by-Step Solution

Answer

The expression simplifies to \(-1.4m\).

Step 1: Identify Like Terms

In the expression \[ -5.7m + 4.3m \]we need to identify like terms. Like terms are terms that have the same variable raised to the same power. Here, both terms have the variable \( m \).

Step 2: Combine Like Terms

Since both terms, \( -5.7m \) and \( 4.3m \), contain the same variable \( m \), they can be combined by adding their coefficients, which gives us\[ (-5.7 + 4.3)m = -1.4m. \]

Step 3: Write the Simplified Expression

The simplified expression is \[ -1.4m. \] The terms have been combined by performing simple arithmetic on the coefficients.

Key Concepts

Like Terms

When simplifying algebraic expressions, the first step is to identify 'like terms.' Like terms are terms that contain the same variable raised to the same power. For example, in the expression \(-5.7m + 4.3m\), both terms have the variable \(m\).

This means they are 'like terms.' Identifying these terms is crucial because it allows you to combine them, simplifying the expression down to fewer terms.

• Like terms have the same variable.
• Like terms have the same exponent or power for the variable.
• Only like terms can be combined in simplification.

Combining Coefficients

Once like terms are identified, the next step is to combine them. In our example, you combine the terms \(-5.7m\) and \(4.3m\) by adding their coefficients. The coefficients in an algebraic expression are the numbers in front of the variables.

In this case, they are \(-5.7\) and \(4.3\). These numbers can simply be added together:

• When adding or subtracting like terms, focus only on the coefficients.
• Place the result in front of the common variable.
• Perform the arithmetic operation as you would with regular numbers.

For example, \[(-5.7 + 4.3)m = -1.4m.\]
Combining coefficients is straightforward—think of it as basic adding or subtracting, just with some algebraic dressing!

Algebraic Simplification

The final step in the process is algebraic simplification. This is where you neatly condense and write the simplified expression using the combined like terms. Simplifying makes the expression easier to read and understand, which is especially helpful in solving equations.

After identifying like terms and combining their coefficients, as in our example, the expression \(-5.7m + 4.3m\) has been simplified to \(-1.4m\). You now use this simplified expression to solve further equations or to understand calculations better.

• Simplification reduces complexity.
• It makes solving algebraic equations more manageable.
• Leads to clearer and more efficient problem solving.

Simplification might seem small, but it is an essential part of working with algebra to get concise expressions that are easy to work with.