# Distributive Property for Multi-Step Equations

More Solving Multi-Step Equations
8:51 — by Marty Brandl

Tip: This isn't the place to ask a question because the teacher can't reply.

## Key Questions

• (I'm assuming you have parenthesis), you take the term right out side the parenthesis and multiply every term in the parenthesis by the outside coefficient. So:

$10 = 4 \left(3 x + 7\right)$ distribute the 4

$10 = 12 x + 28$ subtract 28

$- 18 = 12 x$ divide by 12

$x = - 1.5$

• Whenever an addition or subtraction is present, you have to use the distributive property. When only multiplication or division is involved, you can proceed with division immediately

• In a word, practice.

The distributive property is one of the many ways we can manipulate equations. Later on, you'll have to decide whether using it brings you closer or farther from the solution. But in the case of linear equations with only one variable, it usually doesn't matter whether you use it or not. I'll give an example to demonstrate:

$4 x - 6 = 2 \left(x + 5\right)$

We can start out by using the distributive property to get

$4 x - 6 = 2 x + 10$

We can then group like terms to get:

$2 x = 16$

$\implies x = 8$

Alternatively we can just start with the original problem and bypass the distribution by dividing both sides by 2:

$\frac{4 x - 6}{2} = x + 5$

$2 x - 3 = x + 5$

$\implies x = 8$

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