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Chapter 1: Problem 27

Simplify each expression. $$ (-5.6 x)(-2) $$

Short Answer

Expert verified
The simplified expression is \(11.2x\).

Step by step solution

01

Identify the Expression

The expression given is \((-5.6x)(-2)\). This indicates that there are two parts being multiplied: \(-5.6x\) and \(-2\).
02

Simplify the Coefficients

To simplify the expression, begin by multiplying the coefficients. The coefficient of the first term is \(-5.6\) and the second coefficient is \(-2\). Multiplying these together gives: \(-5.6 \times -2 = 11.2\).
03

Multiply the Variable

Since there is only one variable term \(x\) present in the expression, it remains untouched during multiplication. Therefore, the term simplifies to: \(11.2x\).

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Key Concepts

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

Multiplying Coefficients
When simplifying algebraic expressions, a key step is multiplying the coefficients. Coefficients are the numerical parts of terms in an expression. In this exercise, the coefficients are \(-5.6\) and \(-2\).
To multiply them, simply multiply their absolute values first: \(-5.6 \times 2 = 11.2\). Since both coefficients are negative, multiplying them gives a positive result, yielding \11.2\.
  • Ignore signs initially.
  • Multiply absolute values only.
  • Apply the rule: multiplying two negatives gives a positive.
Variable Terms
Variable terms contain a variable, like \(x\), accompanied by a coefficient. The variable represents an unknown number. In this problem, \(x\) is the variable term coupled with the coefficient \(-5.6\).
It's essential to note that when simplifying, the variable itself is not altered because mathematical operations target the coefficients.
As a result, the term \(-5.6x\) becomes \(11.2x\) after multiplying the coefficients.
Negative Multiplication
Negative multiplication can be a tricky concept for many students. It involves rules that determine the sign of the product based on the signs of the numbers being multiplied.
Here is a simple guide:
  • Negative x Negative: yields a positive product. Example: \((-5.6 \times -2 = 11.2)\).
  • Negative x Positive: results in a negative product. Example: \((-5 \times 3 = -15)\).
  • Positive x Positive: remains positive. Example: \((2 \times 3 = 6)\).
  • Algebra Tip: Always follow the signs strictly; it impacts the final simplified expression.
Algebraic Simplification
Algebraic simplification reduces complex expressions to their simplest form, making them easier to work with. It involves the combination and reduction of like terms.
  • Simplify coefficients first by executing arithmetic operations.
  • Keep the variable term attached to the resulting coefficient.
  • Ensure the expression is as simple as possible, without altering its meaning.
In this exercise, multiplying and simplifying \((-5.6x)(-2)\) led to the simplified \(11.2x\). This demonstrates that simplification involves reducing any given expression, ensuring accuracy using mathematical rules and operations.

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