Solving Equations with 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 solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What are variables in an equation?

Back

Variables are symbols (like x, y, or z) that represent unknown values in mathematical expressions.

Front

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

Back

It means that the variable appears in expressions on both the left and right sides of the equation.

Front

What is the first step in solving an equation with variables on both sides?

Back

The first step is to simplify both sides of the equation if necessary, and then isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

Solve for y: 4y - 8 = 2(y + 6)

Back

y = -8

Front

Solve for z: 5z + 10 = 2(3z + 4)

Back

z = 2

Front

Solve for x: 5x - 14 = 8x + 4

Back

x = -6