Problem 73 Simplify the expression. $$-3(... [FREE SOLUTION]

Chapter 10: Problem 73

Simplify the expression. $$-3(x+1)-2$$

Short Answer

Expert verified

Simplified expression is $-3x-5$.

Step by step solution

Apply the Distributive Property

Start by applying the distributive property, also known as expanding brackets, to the term $-3(x+1)$. This means multiplying $-3$ by both $x$ and $1$, which results in $-3x-3$. So, the expression becomes $-3x-3-2$.

Combine Like Terms

Next, combine the constant terms $-3$ and $-2$, by simple addition of these constants. This results in the simplified expression $-3x-5$.

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Key Concepts

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

Distributive Property

The distributive property is a fundamental concept in algebra that allows us to simplify expressions by eliminating parentheses. It's like unpacking a suitcase: every item inside needs to be considered individually. In algebraic terms, this means that when you have a term outside the parentheses, like

-3 in -3(x + 1), you multiply it by each term inside the parentheses.

For example:

Multiply -3 by x, resulting in -3x.
Multiply -3 by 1, giving -3.

Hence, -3(x + 1) becomes -3x - 3. This method helps both expand and simplify expressions, making them easier to manage in subsequent steps of solving or simplifying equations.

Combining Like Terms

Combining like terms is a key step in simplifying algebraic expressions, allowing us to condense terms that have the same variable and exponent. Think of it as pairing up socks - you can only pair up the socks that are identical. Let's break it down with our previous example:

After applying the distributive property, we ended up with -3x - 3 - 2.
Here, -3x is a variable term while -3 and -2 are constants.
Combining the constants -3 and -2 involves adding them together, resulting in -5.

After this process, the expression is further simplified to -3x - 5.
By managing your like terms correctly, not only do you simplify the expression, but you also reduce the complexity in upcoming equations or functions.

Variables in Algebra

In algebra, variables play a crucial role as they act as placeholders or symbols for unknown values. They allow us to write equations and expressions that can be solved with given numbers. Consider a variable like x in our exercise.

A variable can represent different numbers depending on the context of the problem.
Variables enable us to express general mathematical ideas.

Understanding how to manipulate and work with variables is essential, as it is the primary means through which more complex math problems are navigated. In our example, working with x directly means we focus on operations
involving multiplying, adding, or subtracting it as shown in our application of distributive property and combining like terms processes.

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91影视

Simplify the expression. $$-3(x+1)-2$$

Short Answer

Step by step solution

Apply the Distributive Property

Combine Like Terms

Key Concepts

Distributive Property

Combining Like Terms

Variables in Algebra

One App. One Place for Learning.

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