Problem 38 - Algebra 1: Concepts and Skills

Question

Simplify the expression. $$ 4 g+3+2 g-3 $$

Step-by-Step Solution

Answer

The simplified expression is \(6g\).

Step 1: Identify Like Terms

In this expression, the like terms are the terms which contain the same variable, in this case, 'g'. So, the like terms are '4g' and '2g'.

Step 2: Combine Like Terms

Add the like terms together. This is done by adding the coefficients (the numbers next to the 'g') together. \[4g + 2g = 6g\]

Step 3: Simplify the rest of the expression

After combining like terms, we are left with '+3' and '-3' which are also like terms and they cancel out each other when added together, because 3-3=0.

Step 4: Write the Simplified Expression

With '6g' left from step 2 and '0' left from step 3, our simplified expression is \(6g + 0\). Since adding zero does not change the value, the simplified expression will be \(6g\).

Key Concepts

Combining Like Terms

Understanding how to combine like terms is a fundamental skill in simplifying algebraic expressions. When we talk about like terms, we're referring to terms in an equation that have the same variable raised to the same power. In our example, the like terms are those that involve the variable 'g'.

To combine like terms, you simply add or subtract their coefficients. Coefficients are the numerical part of the terms, and when terms are alike, these numbers can be combined arithmetically. So, for the expression \(4g + 2g\), we add the coefficients 4 and 2 to get 6, and then put this together with the variable 'g' to get \(6g\). This process helps to streamline the expression, making it easier to handle and understand.

Simplifying Algebra

Simplifying algebra equations helps make them more understandable and much less intimidating. The process includes several steps, such as combining like terms, but it also involves eliminating unnecessary parts of the equation.

In the given expression, after combining the like terms containing 'g', we're left with the numerical terms '+3' and '-3'. These are also like terms but without variables. Since they are opposites, they cancel out, simplifying our expression further. This elimination is a part of the simplification process and is essential for acquiring clear and concise results in algebra.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and arithmetic operations. They are the backbone of algebra and are used to represent real-world situations in mathematical terms. An understanding of how to manipulate these expressions is crucial.

In our exercise, \(4g + 3 + 2g - 3\) is an algebraic expression that we simplify by combining like terms and removing any redundancies, which in this case, was the +3 and -3 that cancel each other out. The ability to simplify these expressions not only makes the math easier but also helps students better grasp how algebra can be applied in various contexts.