Solving Equations with Variables on Both Sides

This page focuses on the process of solving equations with variables on both sides. It provides a step-by-step approach to tackle these types of equations, which are common in algebra and higher mathematics.

The main strategy presented is to collect variable terms on one side of the equation and constant terms on the other. This method simplifies the equation and makes it easier to solve for the unknown variable.

Highlight: To solve equations with variables on both sides, collect the variable terms on one side and the constant terms on the other side.

The document presents several examples to illustrate this concept:

1. Solving 15 - 2x = -7x This example demonstrates how to use the Addition Property of Equality to combine like terms and isolate the variable.

2. Solving -2(x - 5) = 6(2 - 0.5x) This more complex example involves using the Distributive Property before applying the steps to solve for x.

3. Solving 3 - 4x = -7 - 4x This example shows a case where the equation has no solution, as it results in a false statement (3 = -7).

Example: In the equation 15 - 2x = -7x, we add 2x to both sides to get 15 = -5x. Then, we divide both sides by -5 to solve for x, resulting in x = -3.

Vocabulary:

• Addition Property of Equality: Adding the same quantity to both sides of an equation maintains the equality.
• Distributive Property: Multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products.

These examples showcase various techniques used in solving multi-step equations with variables on both sides, providing students with a comprehensive understanding of the process. The step-by-step solutions help reinforce the concepts and can be used as a reference when working on similar problems.