Question

Combine like terms: \((2 a+5 b-7)+(a-9 b-6)\). A. \(2 a-4 b-13\) B. \(2 a-4 b+13\) C. \(3 a-4 b-13\) D. \(3 a-4 b+13\)

Short answer

C. \(3a - 4b - 13\)

Step-by-step solution

Distribute and remove parentheses

Start by removing the parentheses in the expression equation: \( (2a + 5b - 7) + (a - 9b - 6) \)

Combine like terms

Group the like terms together: - Terms with 'a': \(2a + a = 3a\)- Terms with 'b': \(5b - 9b = -4b\)- Constant terms: \(-7 - 6 = -13\)

Construct the simplified expression

Use the combined like terms to construct the simplified expression: \(3a - 4b - 13\)

Match with given options

Compare \(3a - 4b - 13\) with the provided options.The correct match is option C.

Key concepts

simplifying algebraic expressions

When simplifying algebraic expressions, the key is to combine like terms. These are terms that have the same variable part, such as \(2a\) and \(a\) or \(5b\) and \(-9b\).

In our exercise, we started with the expression: \((2a + 5b - 7) + (a - 9b - 6)\).
First, we removed the parentheses, resulting in: \(2a + 5b - 7 + a - 9b - 6\).
Then, we grouped the terms with the same variables:
- Terms with 'a': \(2a + a\)
- Terms with 'b': \(5b - 9b\)
- Constant terms: \(-7 - 6\)

Finally, we combined each group of like terms:
- \(2a + a = 3a\)
- \(5b - 9b = -4b\)
- \(-7 - 6 = -13\)

This brought us to our simplified expression: \(3a - 4b - 13\).
This is the essence of simplifying algebraic expressions—combining like terms to make expressions more manageable.

GED mathematical reasoning

The GED test evaluates mathematical reasoning, which is your ability to solve problems involving math in day-to-day situations. A part of this test includes understanding and simplifying algebraic expressions, just like we did in the exercise.
Taking algebraic expressions and making them simpler helps in solving equations and word problems more efficiently.

For the GED, it's important to:
- Understand the basic arithmetic operations: addition, subtraction, multiplication, and division.
- Know how to combine like terms.
- Be able to distribute and simplify expressions.
- Break down complex problems into simpler steps.

By mastering these skills, you'll be able to tackle more complex GED problems with confidence. For example, knowing how to combine like terms as we did in our exercise will allow you to simplify and solve broader mathematical problems.

basic algebra skills

Basic algebra skills are fundamental for solving many types of problems in mathematics. They include understanding variables, constants, and how to manipulate equations.

Basic algebra skills involve steps like:
- Identifying and combining like terms: As we saw, combining \(2a + a\) to get \(3a\) and \(5b - 9b\) to get \(-4b\).
- Handling positive and negative numbers: Subtracting \(-7 - 6\) to get \(-13\).
- Simplifying expressions: Removing parentheses and combining terms to get a simpler form.

These skills help you to solve equations and understand higher-level mathematics. For instance, simplifying \(3a - 4b - 13\) in our exercise is a foundational algebraic operation. Mastery of basic algebra ensures you can approach more advanced math with a solid understanding and problem-solving ability.