Solve Multi-Step Equations

Solve Multi-Step Equations

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:

 $4\left(5x\ +\ 7\right)\ =\ 20x\ +\ 28$  

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:

 $4x\ -\ 5\ +3x\ =\ 7x\ -\ 5$  

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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