Multi-Step Equations (Variables on Both Sides)

A multi-step equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Having variables on both sides of an equation means that the variable appears on both the left and right sides of the equation, requiring manipulation to isolate the variable.

1. Distribute: $$4k - 8 = 2k - 18$$ 2. Move variables to one side: $$4k - 2k = -18 + 8$$ 3. Combine: $$2k = -10$$ 4. Divide: $$k = -5$$ .

The first step is to move all terms involving $$x$$ to one side and constant terms to the other side. This can be done by subtracting $$2x$$ from both sides.

1. Distribute: $$-8p - 16 + p = 4p + 12 + 5$$ 2. Combine like terms: $$-7p - 16 = 4p + 17$$ 3. Move variables to one side: $$-7p - 4p = 17 + 16$$ 4. Combine: $$-11p = 33$$ 5. Divide: $$p = -3$$ .

1. Move $$2k$$ to the left: $$12k - 2k + 15 = 35$$ 2. Combine: $$10k + 15 = 35$$ 3. Subtract 15: $$10k = 20$$ 4. Divide: $$k = 2$$ .

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.

To check your solution, substitute the value back into the original equation to see if both sides are equal.

1. Distribute: $$8a + 12 = -3a + 3 + 31$$ 2. Combine: $$8a + 12 = -3a + 34$$ 3. Move variables: $$8a + 3a = 34 - 12$$ 4. Combine: $$11a = 22$$ 5. Divide: $$a = 2$$ .

A variable is a symbol, often represented by a letter, that stands for an unknown value in an equation.