Problem 30 Simplify. $$ 1 x+2-1 x-3 $... [FREE SOLUTION]

91影视

Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 7: Problem 30

Simplify. $$ 1 x+2-1 x-3 $$

Short Answer

Expert verified

The simplified expression is -1.

Step by step solution

Combine Like Terms

Identify the like terms in the expression. The terms with the variable 'x' are like terms, which are $1x$ and $-1x$. Combining these gives: $1x - 1x$. The constant terms are $2$ and $-3$, which also need to be combined.

Simplify the Expression with Like Terms

Simplify the expression for the like terms: $1x - 1x = 0$. This simplification means the variable terms cancel out. Now, simplify the constant terms: $2 - 3 = -1$.

Write the Final Simplified Form

After simplifying both the like terms and the constants, the expression is reduced to $0 - 1$, which is simply $-1$.

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Key Concepts

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

Understanding Like Terms

When working with algebraic expressions, a crucial concept to grasp is 'like terms.' Like terms have the same variable raised to the same power. For example, in the expression $1x + 2 - 1x - 3$, the terms $1x$ and $-1x$ are considered like terms because they both involve the variable $x$ raised to the first power. Constant terms such as $2$ and $-3$ are also like terms as they don't involve any variable factors. Recognizing like terms is the first step in simplifying an expression because you can then combine them, based on their coefficients and constants.

Combining Like Terms

Once you've recognized the like terms, the next step is to combine them for simplification. Combining involves performing arithmetic operations (addition or subtraction) on the coefficients of the like terms. Take our example $1x + 2 - 1x - 3$:

For the terms involving $x$, which are $1x$ and $-1x$, you simply subtract the coefficients: $1 - 1 = 0$. So these terms cancel each other out completely.
For the constant terms, which are $2$ and $-3$, you perform a subtraction: $2 - 3 = -1$.

By combining like terms in this manner, you're effectively simplifying the expression into a more manageable form.

Algebraic Simplification Made Easy

After you have identified and combined like terms, the next phase is achieving algebraic simplification. The goal here is to express the expression in its simplest form. From our working example $1x + 2 - 1x - 3$, following the steps we've outlined, we reach $0 - 1$. Simplifying this yields $-1$.

This whole process of identifying, combining, and simplifying boils down to reducing the number of terms, removing unnecessary ones, and arriving at a cleaner, more concise expression. When you simplify algebraic expressions correctly, it assists in understanding and solving more complex problems efficiently.

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91影视

Simplify. $$ 1 x+2-1 x-3 $$

Short Answer

Step by step solution

Combine Like Terms

Simplify the Expression with Like Terms

Write the Final Simplified Form

Key Concepts

Understanding Like Terms

Combining Like Terms

Algebraic Simplification Made Easy

One App. One Place for Learning.

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