Problem 84 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 84

Simplify each expression. $$ (-2 x-3)-(x-7) $$

Short Answer

Expert verified

-3x + 4

Step by step solution

- Distribute the negative sign

Distribute the negative sign to each term inside the parenthesis. This makes the expression: (-2x - 3) - (x - 7) = (-2x - 3) - x + 7.

- Combine like terms

Combine the like terms by adding or subtracting the coefficients of the same variable. Here, combine -2x and -x, and combine -3 and 7: (-2x - x) + (-3 + 7).

- Simplify the expression

Simplify by performing the arithmetic: -2x - x = -3x -3 + 7 = 4. So, the simplified expression is -3x + 4.

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Key Concepts

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

Understanding the Distributive Property

The distributive property is a key concept in algebra. It allows us to remove parentheses by distributing a factor to each term within the parentheses. In our example, we started with: $-2x - 3 - (x - 7)$
Notice the negative sign in front of the second parenthesis. We need to distribute it to both $x$ and $-7$
This changes the expression to:
$-2x - 3 - x + 7$
Now, the parentheses are removed, and we can move on to the next step. Remember, correctly applying the distributive property is crucial for simplifying expressions accurately.

Combining Like Terms Effectively

Once we have distributed and removed the parentheses, the next step is to combine like terms. Like terms are terms that contain the same variable raised to the same power. In our expression, the like terms are:

$-2x$ and $-x$
$-3$ and $+7$

We combine the like terms by adding or subtracting them. Let's see this in our example:
$-2x - x + (-3 + 7)$
Combine the $x$ terms: $-2x - x = -3x$
Combine the constant terms: $-3 + 7 = 4$
So, our expression now looks like this: $-3x + 4$
By combining the like terms properly, we simplify the initial expression greatly.

Simplifying with Arithmetic Operations

Simplifying algebraic expressions often involves basic arithmetic operations such as addition and subtraction. Correct usage of these operations ensures the final expression is as simple as possible. In our example, after combining like terms, we ended up with: $-3x + 4$
Here鈥檚 the arithmetic breakdown:

Add $-2x$ with $-x$ to get $-3x$
Add $-3$ to $7$ to get $4$

Thus, our simplified expression $-3x + 4$ makes use of the correct arithmetic operations to reach the final answer. Understanding how to correctly perform these operations ensures efficiency and accuracy in simplifying algebraic expressions.

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91影视

Simplify each expression. $$ (-2 x-3)-(x-7) $$

Short Answer

Step by step solution

- Distribute the negative sign

- Combine like terms

- Simplify the expression

Key Concepts

Understanding the Distributive Property

Combining Like Terms Effectively

Simplifying with Arithmetic Operations

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