Solving Linear Equations

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form $$ax + b = 0$$ , where $$a$$ and $$b$$ are constants.

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side. For example, in $$2x + 3 = 7$$ , subtract 3 from both sides to get $$2x = 4$$ , then divide by 2 to find $$x = 2$$ .

Solving an equation means finding the value(s) of the variable(s) that make the equation true.

The solution is $$x = 5$$ .

The solution is $$x = -1$$ .

The solution is $$x = -8$$ .

The solution is $$x = 2$$ .

The solution is $$x = 10$$ .

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

The first step is to simplify both sides of the equation, if possible, by combining like terms and using the distributive property.