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 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 terms containing the variable 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: 5y + 34 = -2(-7y + 1)

Back

y = 4

Front

What is the first step in solving -8x - 8 + 3(x - 2) = -3x + 2?

Back

Distribute the 3 to both terms inside the parentheses.

Front

Solve: -8x - 8 + 3(x - 2) = -3x + 2

Back

x = -8

Front

What does it mean to distribute in an equation?

Back

To multiply each term inside parentheses by the term outside.

Front

Solve for x: 4(1 - x) + 3x = -2(x + 1)

Back

x = -6

Front

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

Back

To simplify the equation, making it easier to solve.

Front

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

Back

x = 3