Solving Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables (like x or y) 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 variable terms to one side and constant terms to the other. 3. Isolate the variable.

Front

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

Back

y = 4

Front

Solve: 7w + 5 = 3w - 15

Back

w = -5

Front

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

Back

x = 4

Front

Solve: 7x - 4 = 3 + 8x

Back

x = -7

Front

Solve: 14p - 8 = 22 + 20p

Back

p = -5

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

What is a constant in an equation?

Back

A fixed value that does not change, represented by numbers in an equation.

Front

What is the first step in solving the equation 3x + 4 = 10?

Back

Subtract 4 from both sides to isolate the term with the variable.