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Chapter 2: Problem 8

Simplify each expression as completely as possible. $$7+2(x-5)$$

Short Answer

Expert verified
The simplified expression is 2x - 3.

Step by step solution

01

Distribute the constant

Distribute the constant 2 to each term inside the parentheses. The expression becomes: 7 + 2(x - 5) = 7 + 2x - 10
02

Combine like terms

Combine the constant terms 7 and -10. This simplifies to: 7 + 2x - 10 = 2x - 3

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Key Concepts

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

Distributive Property
The distributive property allows us to simplify expressions by distributing a multiplication over an addition or subtraction within parentheses. For example, with the expression \(2(x-5)\), we need to distribute the 2 to both terms inside the parentheses. This means:
  • 2 times x, which is \(2x\)
  • 2 times -5, which is \(-10\)
After distributing, the original expression \(7 + 2(x-5)\) becomes \(7 + 2x - 10\).
This step is essential for making the expression easier to work with in later steps.
Combining Like Terms
Combining like terms means adding or subtracting terms that have the same variables raised to the same power. In our expression \(7 + 2x - 10\), we identify the like terms. The constants 7 and -10 do not have variables, so we can combine them.
Adding these constants together:
  • 7 + (-10) is -3
We keep the \(2x\) as it is since there are no other \(x\) terms.
As a result, the simplified expression becomes \(2x - 3\). Combining like terms helps to condense the expression and make it more straightforward.
Expressions
An expression in algebra is a combination of numbers, variables, and arithmetic operations. For example, in the given problem, our initial expression is \(7 + 2(x - 5)\). Expressions do not include equality or inequality signs.
They can be simplified or manipulated using algebraic rules:
  • Distributive property
  • Combining like terms

Simplifying expressions helps in solving equations later. The goal is to express it in its simplest form, in this case, \(2x - 3\). Mastering these steps provides a strong foundation in algebra for tackling more complex problems.

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Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$-5 s^{2}+3 s t-s^{2}+6 s^{2}$$

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