Problem 69 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(-6-4(y-7)\)

Step-by-Step Solution

Answer

The simplified expression is 22 - 4y.

Step 1: Distribute the negative sign

Distribute the -4 to both terms inside the parentheses: -6 - 4(y - 7) = -6 - 4y + 28.

Step 2: Combine like terms

Combine the constant terms -6 and +28: -6 + 28 = 22. The simplified expression is 22 - 4y.

Key Concepts

Distributive Property

The distributive property is a key concept in algebra. It allows you to multiply a single term by multiple terms inside parentheses. In the exercise, we started with the expression \(-6 - 4(y - 7)\). To simplify, we distribute \(-4\) to both \(y\) and \(-7\):
\-4 * y = -4y
-4 * -7 = 28
So the expression becomes \(-6 - 4y + 28\). Distributing helps break down complex expressions, making them easier to handle.

Combining Like Terms

Combining like terms is an essential process in algebraic simplification. In our expression \(-6 - 4y + 28\), we can only combine the constant terms \(-6\) and \(28\) since they do not have any variables attached. Adding these constants together:
-6 + 28 = 22
This updates our simplified expression to \(22 - 4y\). Remember, like terms are terms with the same variables raised to the same power. Combining these helps simplify your equations and inequalities.

Algebraic Simplification

Algebraic simplification is a step-by-step approach to make expressions easier to work with. By following the steps of distribution and combining like terms, we transformed the expression \(-6 - 4(y - 7)\)into a simpler form \(22 - 4y\). Simplification often involves:
1. Using the distributive property
2. Combining like terms
3. Removing parentheses
This reduces the complexity of solving or studying the expressions. Simplified expressions are more manageable and make further calculations easier.