Solve Multi-Step Equations

Presentation

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Mathematics

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7th - 9th Grade

•

Medium

•

CCSS

6.EE.A.3, 8.EE.C.7B, 7.EE.B.4A

Standards-aligned

Cheryl Nichols

Used 369+ times

FREE Resource

7 Slides • 11 Questions

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

$-2\ =\ a$

$2\ =\ a$

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