Problem 17 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(6+(4-3 x)-8\)

Step-by-Step Solution

Answer

2 - 3x

Step 1 - Simplify Inside the Parentheses

Look inside the parentheses and simplify the expression there first. The expression inside the parentheses is (4 - 3x). Since there are no like terms to combine, the expression remains the same.

Step 2 - Substitute the Simplified Parentheses

Replace the parentheses with the simplified expression. This gives: 6 + (4 - 3x) - 8.

Step 3 - Combine Like Terms

Combine the constants 6, 4, and -8: 6 + 4 - 8 = 2. The expression now is: 2 - 3x.

Key Concepts

Combining Like Terms

In algebra, 'like terms' are terms that have the same variable raised to the same power. For example, in the expression \(5x + 3 + 2x - 1\), the like terms are \(5x\) and \(2x\), as well as \(3\) and \(-1\). Combining like terms helps to simplify the expression by adding or subtracting the coefficients of the like terms. In the example: \(5x + 2x = 7x\) and \(3 - 1 = 2\). Therefore, the simplified expression becomes \(7x + 2\). Remember to always identify and combine the like terms in an algebraic expression. This will make the expression shorter and easier to work with.

Parentheses Simplification

Simplifying expressions inside parentheses is an essential step in algebra. Parentheses are used to indicate that the operations inside them should be performed first. In the provided exercise, the expression inside the parentheses is \(4 - 3x\). Since there are no like terms to combine inside the parentheses, this expression remains as it is. After simplifying or confirming the simplification within the parentheses, you can substitute it back into the overall expression. This helps in reducing the expression step by step. Always handle and simplify the parentheses first to avoid mistakes.

Constants and Variables

In algebra, you will often encounter constants and variables. Constants are fixed values, like \(6, 4,\) and \(-8\) in the provided exercise. They do not change. Variables, on the other hand, are symbols that represent unknown values and can change. For instance, \(x\) in the exercise is a variable. Understanding the difference between constants and variables is crucial, as it helps in combining like terms and simplifying expressions efficiently. In the expression \(6 + (4 - 3x) - 8\), you have constants \(6\), \(4,\) and \(-8\), and the variable \(-3x\). After combining the constants, the expression simplifies to \(2 - 3x\), where \(2\) is a constant and \(-3x\) represents the variable part of the expression.