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Chapter 3: Problem 76

Clear parentheses and combine like terms. $$-2(4 b+3)-10$$

Short Answer

Expert verified
\(-8b - 16\)

Step by step solution

01

- Distribute the Multiplication

Distribute the \(-2\) across the terms inside the parentheses by multiplying \(-2\) by each term. \(-2(4b + 3) = -2 \times 4b + (-2) \times 3 \) This simplifies to \(-8b - 6\).
02

- Combine Like Terms

Now combine the result from Step 1 with the remaining term outside the parentheses, which is \(-10\). \(-8b - 6 - 10\).
03

- Simplify the Expression

Combine numerical constants \(-6\) and \(-10\). \(-8b - 6 - 10 = -8b - 16\).

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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 is a fundamental concept in mathematics that helps simplify expressions. This property states: for any numbers or variables, such as \(a\), \(b\), and \(c\), the expression \(a(b + c)\) is equal to \(ab + ac\). Essentially, you distribute the multiplier (\(a\)) to each term inside the parentheses (\(b\) and \(c\)).

Let's see this in action with the example provided: - Expression: $$ -2(4b + 3)$$- Distribute the \(-2\) to both \(4b\) and \(3\): $$ -2 \times 4b + (-2) \times 3$$- This simplifies to: $$-8b - 6$$ This results in removing the parentheses and breaking down the problem into smaller parts making it easier to manage.
Simplifying Expressions
Simplifying expressions involves making expressions as simple as possible. After distributing terms, the next step is to combine like terms.

In our example, we ended up with: \(-8b - 6\). Now, we need to combine this outcome with the remaining outside term which is \(-10\). This gives us: $$-8b - 6 - 10$$ Like terms are terms that contain the same variable raised to the same power. In this case, we combine numerical constants \(-6\) and \(-10\): $$-8b - 16$$ The expression is now simplified and as simple as possible! Breaking down problems in this manner makes sure every part of the equation is correctly addressed.
Prealgebra
Prealgebra is the foundational stage of learning algebra, focusing on the most basic concepts that prepare you for more advanced topics.

Key topics in prealgebra include:
  • Understanding and using basic arithmetic operations such as addition, subtraction, multiplication, and division.
  • Grasping the concept of variables and simple equations.
  • Learning properties of numbers such as the distributive property, which we've applied in the example.
  • Combining like terms and simplifying expressions.
The sample exercise is a great illustration of prealgebra in action. By understanding how to distribute terms and combine like terms, you build the skill set needed for tackling more complex algebraic expressions in the future.

Mastering prealgebra sets the stage for understanding high-level mathematics. Practice regularly, take each problem step by step, and remember, mathematical concepts are built upon each other. The more you understand the basics, the easier it will be to advance.

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Most popular questions from this chapter

Solve the equation. $$-18=-9 a$$

Clear parentheses and combine like terms. $$2(s+6)-(8 s-t)+6 t$$

Combine the like terms. $$10 x-12 y-4 x-3 y+9$$

Clear parentheses and combine like terms. $$-(8 w+5)+3(w-15)$$

Solve the equation. $$11=s-4$$
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