Problem 128 Simplify. $$9-3(4 y+6)$$... [FREE SOLUTION]

Chapter 4: Problem 128

Simplify. $$9-3(4 y+6)$$

Short Answer

Expert verified

The simplified form of the expression $9-3(4 y+6)$ is $-12y-9$.

Step by step solution

Distribute Multiplication Across Addition

The expression inside the bracket should be distributed across the multiplication i.e. $3 \times 4y$, and $3 \times 6$, respectively. This gives: $9-3(4y+6) = 9-12y-18$

Combine Like Terms

After the distribution you should then combine the like terms, in this case $9$ and $-18$ since they're just numbers without any variable. The resulting expression will be: $9-12y-18 = -12y-9$

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Key Concepts

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

distributive property

When simplifying algebraic expressions, one useful tool is the distributive property. This property states that when you have a multiplication over addition or subtraction inside parentheses, you can "distribute" the multiplication across each term in the parentheses.
For example, in the expression $9 - 3(4y + 6)$, the distributive property lets you multiply $-3$ by both $4y$ and $6$. It breaks down like this:

Multiply $-3$ by $4y$, resulting in $-12y$.
Multiply $-3$ by $6$, resulting in $-18$.

This gives you $9 - 12y - 18$ after distributing.
The distributive property helps to simplify expressions by eliminating parentheses, making it easier to combine like terms later.

combining like terms

Once you have used the distributive property, the next step is to simplify your expression further by combining like terms. Like terms are terms that have the same variable raised to the same power. In our example, $9 - 12y - 18$, you have:

The constant terms $9$ and $-18$
The term $-12y$, which has no "partner" to combine with in this case

You can combine $9$ and $-18$ because they are like terms. When you add them together, you get $-9$.
This gives you the final simplified expression of $-12y - 9$. Combining like terms makes the expression cleaner and easier to handle, especially in solving equations.

linear equations

Linear equations are algebraic equations where each term is either a constant or the product of a constant and a single variable. The expression $-12y - 9$ is part of what could be a linear equation if it were set equal to something, like $-12y - 9 = 0$.
These types of equations have the general form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Linear equations represent straight lines when graphed.
The solutions are the values of the variables that make the equation true.

Simplifying expressions, like with distributive property and combining like terms, prepares you for solving linear equations effectively. Understanding these fundamental steps makes handling more complex algebra easier over time.

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91影视

Simplify. $$9-3(4 y+6)$$

Short Answer

Step by step solution

Distribute Multiplication Across Addition

Combine Like Terms

Key Concepts

distributive property

combining like terms

linear equations

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