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 the left and right sides, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations on both sides of the equation until the variable is alone on one side.

Front

What does it mean to solve an equation?

Back

To find the value(s) of the variable(s) that make the equation true.

Front

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

Back

Subtract 5x from both sides to begin isolating x.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

y = 4.

Front

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

Back

To simplify the equation, making it easier to solve.

Front

What is the solution to the equation 2(4x - 3) - 8 = 4 + 2x?

Back

x = 3.

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

What is the solution to the equation 4(1 - x) + 3x = -2(x + 1)?

Back

x = -6.

Front

What is a common mistake when solving equations with variables on both sides?

Back

Forgetting to perform the same operation on both sides of the equation.