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

To isolate a variable, perform 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 8 - 3a + 12 = 2a?

Back

Combine like terms on the left side: 20 - 3a = 2a.

Front

Solve for a: 8 - 3a + 12 = 2a

Back

a = 4.

Front

What does it mean if an equation has no solutions?

Back

It means there is no value for the variable that can satisfy the equation.

Front

Solve the equation: 24k - 72 = 3(8k - 16)

Back

No solutions.

Front

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

Back

Substitute the solution back into the original equation to verify both sides are equal.

Front

Solve for a: 22 + 2a = 37 + 6 + a

Back

a = 21.

Front

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

Back

Combining like terms simplifies the equation, making it easier to solve.

Front

Solve for x: 10x + 9 = 4x - 9

Back

x = -3.