Equations - Variables on both sides

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the equation contains variables (like x or y) on both the left and right sides, which need to be isolated to solve for the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you 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 3x = 15 - 2x?

Back

The first step is to add 2x to both sides to combine like terms, resulting in 5x = 15.

Front

What is the solution to the equation 3x = 15 - 2x?

Back

x = 3.

Front

How do you solve the equation -4x = 8x + 24?

Back

First, add 4x to both sides to get 0 = 12x + 24, then isolate x.

Front

What is the solution to the equation -4x = 8x + 24?

Back

x = -2.

Front

What does it mean to combine like terms in an equation?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

How do you solve the equation 7x - 11 = 5x + 25?

Back

First, subtract 5x from both sides to get 2x - 11 = 25, then add 11 to both sides and divide by 2.

Front

What is the solution to the equation 7x - 11 = 5x + 25?

Back

x = 18.