Solving Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation where the variable appears on both sides of the equal sign, requiring manipulation to isolate the variable.

Front

How do you solve an equation with variables on both sides?

Back

1. Simplify both sides if necessary. 2. Move all terms containing the variable to one side and constant terms to the other. 3. Isolate the variable.

Front

Solve for x: 12x - 15 = 3(2x + 3)

Back

x = 4

Front

Solve for x: 7x - 4 = 3 + 8x

Back

x = -7

Front

Solve for x: 7x = 4x + 33

Back

x = 11

Front

Solve for x: 5x - 14 = 8x + 4

Back

x = -6

Front

Solve for y: 5y + 34 = -2(-7y + 1)

Back

y = 4

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is alone on one side of the equation, making it easier to solve.

Front

What is the first step in solving the equation 5x - 14 = 8x + 4?

Back

Subtract 5x from both sides to start isolating x.

Front

What is a common mistake when solving equations with variables on both sides?

Back

Forgetting to apply the same operation to both sides of the equation, which can lead to incorrect solutions.