Multi-Step Equations

Solve Multi-Step Equations

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An Equation is a statement that says both sides of the equal sign are equivalent, or the same.

Here are the steps in solving a multi-step equation:

• Distributive Property

• Combine like terms (on the same side of the equation)

• Use inverse operations to put variables and constants on opposite sides of the equation.

• Isolate the variable

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.

It looks like this:

Multiple Choice

Let's try it. Which answer shows an equivalent expression created with the Distributive Property?

$$8\left(5\ +\ 7x\right)$$  

• 40 + 56x

• 40 + 7x

• (40 + 56x)

Multiple Choice

Try another one. It can get tricky when there are negatives.

$$-6\left(4x\ -\ 3\right)$$  

• $$-24x\ +\ 18$$  

• $$-24x\ -\ 18$$  

• $$24x\ +\ 18$$  

• $$-24x\ -\ 3$$  

Multiple Choice

One more. What should we do when we only see a negative sign and no integer?

$$-\left(5\ -\ 6x\right)$$  

• $$-5\ +\ 6x$$  

• $$-5\ -\ 6x$$  

• $$5\ +\ 6x$$  

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

$$4\left(2\ +\ 3x\right)\ =\ 56$$  

• $$8\ +\ 12x\ =\ 56$$  

• $$8\ +\ 3x\ =\ 56$$  

Multiple Choice

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

$$4\left(2\ +\ 3x\right)\ =\ 56$$  

• $$x\ =\ 4$$  

• $$x\ =\ 3$$  

Multiple Choice

What will this equation look like after you have simplified?

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

• $$-29\ =\ 10\ a\ -\ 5\ +\ 2a$$  

• $$-29\ =\ 12a\ -\ 5$$  

Multiple Choice

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

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

• $$-2\ =\ a$$  

• $$2\ =\ a$$  

Open Ended

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