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 of the equation. 2. Move all variable terms to one side and constant terms to the other. 3. 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, making it easy to determine its value.

Front

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

Back

x = -7

Front

Solve the equation: 5x - 14 = 8x + 4

Back

x = -6

Front

What is the first step in solving the equation -6(1 - 6r) = -2(r + 3)?

Back

Distribute the -6 and -2 to simplify both sides of the equation.

Front

What is the solution to the equation 3 - 5x = -9 + x?

Back

x = 2

Front

What does it mean to check your solution in an equation?

Back

To substitute the solution back into the original equation to verify that both sides are equal.

Front

What is the importance of combining like terms in an equation?

Back

Combining like terms simplifies 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.