Problem 57 Rewrite each expression using th... [FREE SOLUTION]

Chapter 1: Problem 57

Rewrite each expression using the distributive property. Simplify if possible. $$2(-6+5+3)$$

Short Answer

Expert verified

Using the distributive property, we can rewrite the given expression as: $2(-6) + 2(5) + 2(3)$ Then, perform multiplication and simplify to get: $-12 + 10 + 6 = 4$

Step by step solution

Identify the terms inside the parentheses

In our given expression, we have three terms inside the parentheses: $-6$, $5$, and $3$.

Apply distributive property

Now, we will multiply each term inside the parentheses by the number outside, which is $2$. We can write this as: $2(-6) + 2(5) + 2(3)$

Multiply

Perform multiplication for each term: $-12 + 10 + 6$

Simplify and find the final answer

Add the numbers to simplify the expression: $-12 + 10 + 6 = -2 + 6 = 4$ So, the simplified expression after using the distributive property is $4$.

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Key Concepts

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

Algebraic Expressions

Algebraic expressions are a fundamental part of algebra. They consist of numbers, variables, and operators. An algebraic expression can represent a single value or a set of values.
Understanding these expressions is crucial in solving mathematical problems as they form the basis of equations and inequalities.

Numbers: These represent specific values within the expression.
Variables: These are symbols (like x or y) that stand in for unknown values or changing quantities.
Operators: Symbols such as +, -, *, and / that define operations applied to numbers and variables.

Breaking down an algebraic expression is the first step in understanding or manipulating it. For instance, in the exercise given,
the expression $2(-6+5+3)$ consists of a number (2), and terms within parentheses to be distributed.
This expression can be understood and used once we breakdown and simplify it using algebraic properties like the distributive property.

Simplification

Simplification is the process of reducing an expression to its simplest form. This often involves combining like terms and performing basic arithmetic calculations. The goal is to make the expression as clear and concise as possible.
In our example, $2(-6+5+3)$, simplification involves using arithmetic operations after applying the distributive property to make the expression easier to work with.

Distribute: Multiply each term inside the parentheses by the number outside. In our case: $2(-6), 2(5), 2(3)$.
Perform Arithmetic: Carry out the multiplications: $-12, 10, 6$.
Combine Like Terms: Add or subtract these values to simplify: $-12 + 10 + 6$.

This simplification helps us reach the final answer efficiently, which in this example, is the value $4$. This straightforward result is much easier to interpret and communicate.

Problem-Solving Steps

Problem-solving in algebra often involves a series of logical steps to arrive at a solution. These steps help structure your approach to breaking down complex expressions or equations.
Let's break down the problem-solving steps used in handling the expression $2(-6+5+3)$ using the distributive property.

Identify Components: Recognize the terms and numbers involved in the expression. Here, it's important to note the
outer number (2) and the inner terms (-6, 5, 3).
Apply Algebraic Properties: Use the distributive property to handle each term individually. This involves expanding
the expression from $2(-6+5+3)$ to separate terms like $2(-6) + 2(5) + 2(3)$.
Solve Each Part: Perform individual calculations, which are $-12, 10, 6$ in this problem.
Simplify: Finally, add the results together to solve the expression, which simplifies to $4$.

Following these steps allows for an organized means of solving expressions, ensuring clarity and ensuring no part of the problem is overlooked. This structured approach is key in mastering algebraic solving techniques.

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91影视

Rewrite each expression using the distributive property. Simplify if possible. $$2(-6+5+3)$$

Short Answer

Step by step solution

Identify the terms inside the parentheses

Apply distributive property

Multiply

Simplify and find the final answer

Key Concepts

Algebraic Expressions

Simplification

Problem-Solving Steps

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