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Chapter 2: Problem 55

Simplify each algebraic expression by combining similar terms. $$x-0.4 x-1.8 x$$

Short Answer

Expert verified
The simplified expression is \(-1.2x\).

Step by step solution

01

Identify Like Terms

To simplify the expression, first identify like terms. In the expression \(x - 0.4x - 1.8x\), all the terms are like terms because they all involve the variable \(x\).
02

Combine Like Terms

Combine the like terms by adding or subtracting their coefficients. The expression \(x - 0.4x - 1.8x\) can be rewritten by combining the coefficients:The coefficient of \(x\) is 1, the coefficient of \( -0.4x\) is -0.4, and the coefficient of \(-1.8x\) is -1.8. So, the combined coefficient becomes:\[1 - 0.4 - 1.8 = -1.2\]
03

Write the Simplified Expression

Multiply the combined coefficient by \(x\) to get the simplified expression, which is:\(-1.2x\).

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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, identifying like terms is crucial. Like terms are terms that contain the same variable raised to the same power. It means their variable components must be identical.

For example, in the expression \(x - 0.4x - 1.8x\), the variable in each term is \(x\). This makes them like terms, because they all share the same variable but may have different coefficients. Recognizing which terms are alike helps in combining them to simplify expressions efficiently.

Remember:
  • Like terms must have the same variable(s).
  • They should also have the same exponent on those variables.
  • Constants (like \(5\) or \(-3\)) are also considered like terms.
Deciphering Coefficients
Coefficients play a significant role in algebraic expressions. They are the numerical factors that multiply the variable in a term.

In our example of \(x - 0.4x - 1.8x\), the coefficients are :
  • 1 for \(x\),
  • -0.4 for \(-0.4x\), and
  • -1.8 for \(-1.8x\).
To simplify expressions, it is essential to add or subtract the coefficients of like terms. It is similar to adding or subtracting regular numbers but keeping the variable part intact.
An easy method to handle coefficients:
  • Identify them alongside their respective terms.
  • Pay attention to their signs (positive or negative).
  • Perform the arithmetic operation to combine them.
Simplifying Expressions
Simplifying an expression is the process of combining like terms and condensing the expression to its simplest form.

In our example, to simplify \(x - 0.4x - 1.8x\), follow these steps:
  • Identify the like terms, which are all terms involving \(x\).
  • Combine the coefficients: \(1 - 0.4 - 1.8 = -1.2\).
  • Write the simplified expression as \(-1.2x\).

It reduces the expression to fewer terms, making it easier to manage and understand. Avoid confusion by consistently checking your steps and ensuring all like terms have been combined.
Benefits of simplifying expressions include:
  • Reduced complexity and potential for mistakes in calculations.
  • Easier interpretation and application in further mathematics problems.

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Most popular questions from this chapter

Perform the indicated operations. $$5.92 \div(-0.8)$$

Tanya bought 400 shares of one stock at \(\$ 14.78\) per share, and 250 shares of another stock at \(\$ 16.36\) per share. How much did she pay for the 650 shares?

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