Using Distribution to Balance Expressions

Let's look at this equation. The expression x + 3 is being multiplied by 7. To isolate the variable, we need to undo that multiplication. The opposite of multiplying by 7 is dividing by 7.

So, we would divide both sides by 7.

Dividing by 7 works, but it requires calculating 91 / 7. Let's learn a new skill for these situations.

Here we're asked what balances two groups of C + 3 S. Think of this as unpacking the boxes on the left. Each box contains one C and 3 S. If we take everything out of the two boxes, we'll have 2 C in total. We'll also have two groups of three S's, which is 6 S altogether.

So two groups of C plus 3 S equals 2 C + 6 S. This is the distributive property.

What balances four groups of t + 5? We can distribute the four to each term inside the parenthesis. First we have four groups of t or 4 t. Then we have four groups of five which gives us 20.

So four groups of t + 5 can be rewritten as 4 t + 20.

Here's another example. What balances two groups of 3 C + 7? Let's distribute the two.

2 * 3 C gives us 6 C. Next, 2 * 7 gives us 14. So, two groups of 3 C + 7 = 6 C + 14.

Let's do one more. This time we have three groups of 3 S + T. Applying the distributive property again, we multiply the 3 by each term inside. 3 * 3 s gives us 9 s and 3 * t gives us 3t. Our rewritten expression is 9 s + 3 t.

We've learned how to rewrite expressions by unpacking them using the distributive property. Instead of dividing first, we can multiply the number outside the parenthesis by each term inside. This changes the equation into a different but equivalent form, which should make it easier to solve.