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 sides of the equal sign, 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: 7x = 3x + 24?

Back

Subtract 3x from both sides to get 4x = 24.

Front

What does it mean to 'get the variable on one side'?

Back

It means to rearrange the equation so that all terms containing the variable are on one side and constant terms are on the other.

Front

Solve for x: 7x - 4 = 3 + 8x

Back

x = -7.

Front

What is the solution to the equation: 14p - 8 = 22 + 20p?

Back

p = -5.

Front

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

Back

To simplify the equation, making it easier to solve for the variable.

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

Solve for f: f - 4 = 6f + 26

Back

f = -6.

Front

What is the importance of maintaining balance in an equation?

Back

Any operation performed on one side must also be performed on the other side to keep the equation true.