By Karen L. Anglin

I take advantage of this booklet to coach arithmetic vocabulary in my pre-algebra and algebra sessions. It is going well past the textbook addition, subtraction, and so on. phrases. It discusses turn-around phrases, comma placement, parentheses, and so on. nice origin for be aware difficulties.

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**Example text**

Example 10: Solve the following equation: 3(2x – 1) = 4x + 1 1. Distribute. 6x – 3 = 4x + 1 There was no need to combine like terms because there are no like terms in each expression. 2a. Move variables to the left side of the equation. In this example, add –4x to each side of the equation. 6x – 3 + –4x = 4x + 1 + –4x 2b. Place like terms adjacent to each other and simplify. Note: Subtracting 3 is changed to adding –3. The commutative property of addition works only if all operations are addition.

Now combine like terms: –2x – 12. This is the simplified expression. While a problem such as Example 8 does not seem difficult, if the order is changed slightly, the distribution is not as obvious, as shown in Example 9. Example 9: Simplify the following: –7 – 2(x + 3) A common error is to distribute a +2. A –2 must be distributed throughout the parentheses because the entire expression is subtracted from –7. If you distribute a +2, the expression will be incorrect because you will add 6 instead of subtracting 6.

Check more of your translation abilities with Example 3. Example 3: Translate the following statement into an equation: The product of eight and a number yields twenty-four. What operation should replace AND in this equation? The leading keyword, PRODUCT OF, indicates the eight is multiplied by a number. The product of eight and a number yields twenty-four Note: The first expression is translated, then the equal sign is translated, and then the expression on the right of the equal sign. Often, in mathematics, breaking the problem up into smaller pieces can increase your success.