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Chapter 1: Problem 47

Simplify each expression. $$ -2 x+3+4 x-17+20 $$

Short Answer

Expert verified
The simplified expression is \(2x + 6\).

Step by step solution

01

Identify Like Terms

Group the like terms together. In this case, the like terms are \(-2x\) and \(4x\) for the variable part, and \(3\), \(-17\), and \(20\) for the constant part.
02

Combine Like Terms (Variable Part)

Add the coefficients of the variable part: \(-2x\) and \(4x\). Thus, \(-2x + 4x = 2x\).
03

Combine Like Terms (Constant Part)

Add the constants together: \(3 - 17 + 20\). Thus, \(3 - 17 = -14\) and \(-14 + 20 = 6\).
04

Write the Simplified Expression

Combine the simplified variable part and the constant part to write the final simplified expression: \(2x + 6\).

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Key Concepts

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

Combining Like Terms
When simplifying an expression, one of the fundamental steps is combining like terms. Like terms are terms that have the same variables raised to the same power. In the given problem ewline -2x + 3 + 4x - 17 + 20, ewline we have two types of terms: terms with the variable 'x' and constant terms. To start simplifying, group the like terms together. Here are the groups:
  • Variable terms: ewline -2x and 4x
  • Constant terms: ewline 3, -17, and 20
By grouping these like terms, you are setting yourself up to combine them more straightforwardly. This process helps in making the simplification clearer and prevents confusion.
Coefficients
Understanding coefficients is vital when simplifying expressions. A coefficient is a numerical factor in a term that includes a variable. For instance, in -2x,ewline the coefficient of 'x' is -2. Similarly, in 4x, ewline the coefficient is 4. When combining like terms, you add or subtract the coefficients of those terms. For the variable terms in our exercise, we have: -2x + 4x. You only combine the coefficients here:ewline -2 + 4 = 2. Thus, the terms simplify to ewline 2x. This method helps ensure you don't mix up the coefficients and the constants.
Constants
Constants are numbers without variables. They stand alone and don't change regardless of the value of any variables within the expression. In our example, 3, -17, and 20 are the constants.Combining constants is straightforward. You simply add or subtract them as you would with any regular numbers. Let's break it down:
  • First, combine 3 and -17: ewline 3 - 17 = -14
  • Next, add -14 and 20: ewline -14 + 20 = 6
So, the simplified form of the constant terms is 6. Now, you combine the simplified variable part ( 2x ) with the simplified constant part ( 6 ), resulting in: 2x + 6. By understanding and combining constants accurately, you ensure your expression is fully simplified and correct.

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Most popular questions from this chapter

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