Question

Select the expression equivalent to \(2(3+5-4)\). A. \(5+1\) B. \(6+1\) C. \(5+7-6\) D. \(6+10-8\)

Short answer

D. \(6 + 10 - 8\)

Step-by-step solution

- Simplify Inside the Parentheses

Evaluate the expression inside the parentheses first: \(3 + 5 - 4\). Calculate \(3 + 5\) to get \(8\). Then subtract \(4\) from \(8\) which results in \(4\). This simplifies the expression to \(2 \times 4\).

- Multiply the Simplified Value

Next, multiply \(2\) by the simplified value from Step 1. Calculate \(2 \times 4\) to get \(8\). The expression simplifies to \(8\).

- Find the Equivalent Expression

Compare the result with the available options:\(5+1 = 6\), \(6+1 = 7\), \(5+7-6 = 6\), \(6+10-8 = 8\). The equivalent expression is \(6+10-8\).

Key concepts

Simplifying Expressions

Simplifying expressions is a fundamental skill in algebra. The goal is to make the expression as simple as possible. This usually means performing operations like addition, subtraction, multiplication, and division.
Simplifying an expression often involves combining like terms and performing arithmetic operations. For example, in the given problem, you simplify inside the parentheses first and then perform multiplication.
Here are some simple rules to remember:

• Combine like terms.
• Perform any operations inside parentheses first.
• Use arithmetic operations to simplify further.

Order of Operations

The order of operations is crucial in simplifying expressions correctly.
If operations are performed in the wrong order, the result can be incorrect. The commonly remembered acronym for the order of operations is PEMDAS, which stands for:

• P - Parentheses first
• E - Exponents (i.e. powers and square roots, etc.)
• M/D - Multiplication and Division (left-to-right)
• A/S - Addition and Subtraction (left-to-right)

For the given exercise, you would first perform the operations inside the parentheses. In this case, you add and subtract within the parentheses and then multiply by 2.
Always remember to follow this order to simplify accurately.
For example, in the given problem:

• You simplify the expression inside the parentheses first: \(3 + 5 - 4 = 4\).
• Next, you multiply 2 by the result inside the parentheses: \(2 \times 4 = 8\).

GED Math Prep

GED Math Prep involves practicing various math concepts that will help you pass the General Educational Development (GED) test.
One major concept in GED math is simplifying algebraic expressions and using the order of operations correctly.
To be good at GED math, it's helpful to:

• Practice a lot of problems involving these concepts.
• Review the basics of arithmetic, fractions, and algebra.
• Use online resources and practice tests to gauge your understanding.

For example, to solve the exercise given, you need to:

• Understand how to operate inside parentheses: \(3 + 5 - 4 = 4\).
• Multiply the result by an outside factor: \(2 \times 4 = 8\).

Recognize and match your simplified result with an equivalent expression from the options provided.
Regular practice builds the confidence and skill required to solve algebraic problems accurately.