Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 5x - 14 = 8x + 4?

Back

Subtract 5x from both sides to begin isolating the variable.

Front

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

Back

x = -6

Front

What does it mean to combine like terms in an equation?

Back

It means to simplify the equation by adding or subtracting terms that have the same variable and exponent.

Front

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

Back

x = -7

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation.

Front

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

Back

w = -5

Front

What is the significance of the equal sign in an equation?

Back

It indicates that the expressions on both sides have the same value.

Front

How do you handle negative numbers when solving equations?

Back

Apply the same rules of arithmetic, ensuring to maintain the signs correctly.