Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

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

Front

What is the first step to solve an equation with variables on both sides?

Back

Combine like terms on both sides of the equation.

Front

Solve for n: 1 + 4n - 6n = 1 - 8n

Back

Combine like terms: -2n = -8n; then add 8n to both sides: 6n = 0; n = 0.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

Solve for m: 9m + 14 = 2m

Back

Subtract 2m from both sides: 7m + 14 = 0; then subtract 14: 7m = -14; m = -2.

Front

What is the solution to the equation 3y + 16 = 5y?

Back

y = 8.

Front

How do you isolate a variable in an equation?

Back

Perform inverse operations to move all terms involving the variable to one side and constant terms to the other.

Front

Solve for x: 4(1-x) + 3x = -2(x+1)

Back

x = -6.

Front

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

Back

Checking ensures that the solution satisfies the original equation, confirming its validity.

Front

Solve for z: 11z - 5 = 9z + 7

Back

Subtract 9z from both sides: 2z - 5 = 7; then add 5: 2z = 12; z = 6.