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. Move all terms containing the variable to one side of the equation. 2. Move constant terms to the other side. 3. Simplify and solve for the variable.

Front

Solve the equation: 7x - 4 = 3 + 8x

Back

x = -7

Front

Solve the equation: 8x - 8 = -4x + 16

Back

x = 2

Front

Solve the equation: 7w + 5 = 3w - 15

Back

w = -5

Front

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

Back

y = 4

Front

Solve the equation: 2(4x - 3) - 8 = 4 + 2x

Back

x = 3

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 a constant in an equation?

Back

A fixed value that does not change, represented by a number.

Front

What is the first step in solving the equation 3x + 5 = 2x + 10?

Back

Subtract 2x from both sides to get x + 5 = 10.