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Chapter 5: Problem 31

Subtract. $$ (5 x-3)-(2 x-1) $$

Short Answer

Expert verified
The result of the subtraction is \(3x - 2\).

Step by step solution

01

Distribute the Negative Sign

To subtract the expressions, distribute the negative sign across the second expression. This modifies the expression to: (5x - 3) - (2x - 1) becomes (5x - 3) - 2x + 1.
02

Combine Like Terms

Now, combine the like terms, which are the expression terms that have the same variable. First, look at the terms with the variable "x": 5x - 2x = 3x. Next, combine the constant terms: -3 + 1 = -2.
03

Write the Simplified Expression

With the like terms combined, write down the simplified form of the expression: 3x - 2.

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Key Concepts

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

Expression Simplification
Simplifying an expression in algebra means rewriting it in a more understandable or compact form. This process helps to solve equations more easily and compare different expressions.
Start by breaking down complex parts into simpler terms. This may involve several steps, including distribution and combining like terms.
Simplification often makes equations more manageable, reducing errors in further calculations. **The goal is clarity**, so always aim for the most straightforward form.
Combining Like Terms
Like terms are terms within an expression that have the same variable raised to the same power. For instance, in the expression \(5x - 2x + 3\), both \(5x\) and \(2x\) are like terms because they share the variable \(x\).
Combining like terms involves
  • Adding or subtracting their coefficients while retaining the common variable.
  • Simplifying the expression by grouping these terms together.
For example, **adding** \(5x - 2x\) results in \(3x\). This step brings clarity and reduces complexity in algebra.
Distributive Property
The distributive property is a key algebraic principle used to multiply a single term across multiple terms inside parentheses. Its basic formula is \(a(b + c) = ab + ac\).
When subtracting expressions, distributing the negative sign is crucial to maintain the balance of the equation.
  • **Apply the negative sign** to each term inside the parentheses.
  • For example, \((5x - 3) - (2x - 1)\) turns into \((5x - 3) - 2x + 1\).
This step ensures that all terms are correctly modified, setting up accurate simplification.

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