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Chapter 7: Problem 126

In the following exercises, simplify using the distributive property. $$4-11(3 c-2)$$

Short Answer

Expert verified
Simplified expression is $$26 - 33c$$.

Step by step solution

01

Identify the expression inside the parentheses

The given expression is: your job is to identify the part inside the parentheses, which is $$3c - 2$$
02

Multiply each term inside the parentheses by -11

Applying the distributive property, multiply $$-11$$ by each term in $$3c - 2$$: $$-11 \times 3c = -33c$$ $$-11 \times -2 = 22$$
03

Simplify the expression

Rewrite the expression by combining the distributed terms with the initial constant:$$4 - 33c + 22$$. Combine like terms, specifically the constants:$$4 + 22 = 26$$. Therefore, the simplified expression is:$$26 - 33c$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions is a key concept in algebra. It helps make equations easier to work with. In our problem, we used the distributive property to simplify the expression. The distributive property allows us to multiply a single term by each term inside the parentheses separately.
For example: If you have $$a(b + c)$$, you distribute by multiplying $$a$$ with both $$b$$ and $$c$$, which gives you $$ab + ac$$.
In our exercise, we distributed the \(-11\) across the terms inside the parentheses: $$-11(3c - 2) = -33c + 22$$. This makes the expression simpler to handle in further steps.
Prealgebra Concepts
Understanding prealgebra concepts is essential before moving to advanced algebra. One fundamental idea is the use of the distributive property. This allows us to break down more complex expressions into simpler parts. Another prealgebra concept seen in this problem is the operation of negative numbers.
For example: When we multiply \(-11\) by \(3c\), we get \(-33c\). Similarly, multiplying $$-11$$ by $$-2$$ results in $$22$$ because a negative times a negative gives a positive.
Recognizing these basic rules helps you solve algebraic problems easily and correctly.
Combining Like Terms
Combining like terms is another critical skill in algebra. It means simplifying expressions by merging terms that have the same variable or are constants.
For example: In our simplified expression $$4 - 33c + 22$$, we have like terms \(4\) and \(22\), both being constants.
We combine them by adding: \(4 + 22 = 26\). So, the expression \(4 - 33c + 22\) becomes \(26 - 33c\).
This makes the expression easier to understand and use in solving equations.

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