Solving Multi-step Equations Pt. 1

Solving Multi-step Equations Pt. 1

by Rupert Cox

Let's review inverse operations

addition <--> subtraction

multiplication <--> division

Use the inverse to "move" a term to the other side of the equation!

How do I solve multi-step equations?

• Simplify first.

• Look over the equation and decide the next steps.

What do you mean by simplify?

• Resolve parentheses using the Distributive Property.

• Combine like terms on the same side of the equation.

How do I simplify using the Distributive Property?

• Multiply the term on the outside of the parentheses times each term on the inside of the parentheses.

• Drop the parentheses.

Multiple Choice

It can get tricky when there are negatives.

$$-6\left(4x\ -\ 3\right)$$  

• $$-24x\ +\ 18$$  

• $$-24x\ -\ 18$$  

• $$24x\ +\ 18$$  

• $$-24x\ -\ 3$$  

Simplifying an Eq. with distributive looks like this:

Multiple Choice

Now let's apply it to an equation. What will this equation look like after you simplify it?

$$4\left(2\ +\ 3x\right)\ =\ 56$$  

• $$8\ +\ 12x\ =\ 56$$  

• $$8\ +\ 3x\ =\ 56$$  

How do I combine like terms on the same side of the equal sign?

• Add or subtract them as if the equal sign were not there.

• Remember that you should NOT use inverse operations or opposites to combine like terms on the same side of the equal sign.

It looks like this:

Multiple Choice

Let's try it. Which answer choice shows the correct way to combine like terms here?

$$5\ -\ 7x\ -\ 2\$$  

• $$3\ -\ 7x$$  

• $$5\ -\ 5x$$  

Multiple Choice

Now solve your simplified equation. What is the solution for:

$$-29\ =\ 5\left(2a\ -1\right)\ +\ 2a$$  

• $$-2\ =\ a$$  

• $$2\ =\ a$$  

Multiple Choice

What will this equation look like after you have simplified?

$$-29\ =\ 5\left(2a\ -\ 1\right)\ +\ 2a$$  

• $$-29\ =\ 10\ a\ -\ 5\ +\ 2a$$  

• $$-29\ =\ 12a\ -\ 5$$  

FOLLOW THESE STEPS!

Start at the first checkbox.

Work your way down the steps.

Don't stop until the variable is ALL BY ITSELF!

Multiple Choice

Now solve your simplified equation. What is the solution for:

$$4\left(2\ +\ 3x\right)\ =\ 56$$  

• $$x\ =\ 4$$  

• $$x\ =\ 3$$