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

How do you solve the equation 6z = 49 - z?

Back

Add z to both sides to get 7z = 49, then divide by 7 to find z = 7.

Front

What is the first step to solve 5x - 14 = 8x + 4?

Back

Rearrange the equation by moving all terms involving x to one side and constant terms to the other.

Front

What is the solution for y in the equation 2y + 3 = y + 5?

Back

Subtract y from both sides to get y + 3 = 5, then subtract 3 to find y = 2.

Front

How do you isolate the variable in the equation 28 + 3r = 10r?

Back

Subtract 3r from both sides to get 28 = 7r, then divide by 7 to find r = 4.

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is alone on one side, making it easy to find its value.

Front

What is the solution to the equation 7(p + 9) = -21?

Back

First, divide both sides by 7 to get p + 9 = -3, then subtract 9 to find p = -12.

Front

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

Back

To verify that the solution satisfies the original equation, ensuring it is correct.

Front

What is a linear equation?

Back

An equation that graphs as a straight line, typically in the form y = mx + b.

Front

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

Back

Adding or subtracting terms that have the same variable and exponent to simplify the equation.