Solving Multi-Step Equations Foundations of Algebra

A Multi-Step Equation A multi-step equation is an equation that requires more than one step to solve for the variable. The problem will contain more than one operation. To solve the equation: undo the operations that are being performed on the variable, starting with the one farthest away.

A Good First Step A good first step is to try to combine like terms. Like terms are… constants (example: 5 and -3) coefficients and variables (ex: 3x and x)

Combining Like Terms Remember! You cannot combine terms through addition or subtraction of non-like terms! For example, you cannot add 5+x and get 5x. You can add… 5x+3x=8x (5x and 3x are like terms)

Example In this example, the 4 and 5 are like terms. They can be combined to get 9. Now you have a one-step equation! Solve by subtracting the 9 on both sides.

Example In this example, the 4x and 3x are like terms. They can be combined to get 1x. Now you have a one-step equation! Solve by subtracting the 2 on both sides.

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Fractions Example Don’t forget, these are like terms and can be combined! When you combine fractions you need to get a common denominator. What is it? 6!

Solve for x.

What if it’s not on the same side? When solving an equation with variables on both sides of the equal sign, you must move the smaller variable term to the other side. This is done with addition or subtraction, depending on the sign of the term.

For example… In this example the 5x and 17 x are like terms. Solve by subtracting the 5x on both sides. Now you have a one-step equation! Finish by dividing both sides by 12!

Solve.

Solve.

Solve.

Some problems need… DISTRIBUTION!

How do you know? Problems that need distribution will have parentheses. Distribute numbers through the parenthesis and then combine like terms to solve. When you “distribute” the numbers, you are actually multiplying the number outside the parenthesis into each term inside.

What to remember! When you distribute, remember to keep the sign (addition or subtraction) that is holding the terms in the parenthesis together. For example… When you distribute the 2, you get 2x – 6. The subtraction sign is still there!

Example You can finish the problem then!

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Solve.

Solve. Hate decimals? Here’s a trick! Multiply EVERYTHING by 10!