Equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, 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 variable terms to one side and constant terms to the other. 3. Combine like terms. 4. Isolate the variable.

Front

What does it mean to isolate a variable?

Back

To manipulate an equation so that the variable is alone on one side of the equation.

Front

Solve: 8w - 8 = -4x + 16

Back

x = 2

Front

Solve: -6(1 - 6r) = -2(r + 3)

Back

r = 0

Front

Solve: 2x = x + 3

Back

x = 3

Front

Solve: 7x = 4x + 33

Back

x = 11

Front

What is a constant in an equation?

Back

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

Front

What is a coefficient?

Back

A numerical factor that multiplies a variable in an algebraic expression.

Front

What does it mean for an equation to be balanced?

Back

Both sides of the equation have the same value, meaning any operation performed on one side must also be performed on the other.