Mental Shortcuts for Algebra 1

Most people who need Algebra 1 help have problems moving terms around in expressions and equations. This comes from a lack of practical experience in dealing with these types of situations, which is typical of people who are learning Algebra 1 for the first time. It’s unfair to expect students to have experience with something that they’ve never learned, so here we’re going to show a couple of quick shortcuts that can help you with common tasks in algebra.

Rearranging Terms in an Expression

The key idea here is that every term will keep the sign that’s in front of it when you’re rearranging terms. For example, in the expression -3 + 2 + 5 – 4 the negative sign will stay with the 3 and 4 no matter how you arrange the four terms, and the positive sign will stay with the 2 and 5. This means you could rewrite the expression at 5 – 3 – 4 + 2 or -4 + 5 + 2 – 3 or any combination of the four terms. In Algebra 1, you’ll often need to rewrite an expression so that the terms are in a specific order. This shortcut can help you to do that quickly and easily without any confusion.

Rearranging Terms in an Equation

Moving around the terms of an equation is exactly the same as moving around the terms of a single expression, with one change. When you move a term across an equals sign, the sign of that term changes. For example, if we have something like 2x – 5 = 13 and we want to move the term -5 to the right side of the equation, we would change the sign so it’s positive and we could have 2x = 5 + 13 or 2x = 13 + 5. Note that if we moved the term -5 so that it was on the far left side of the equation, the sign wouldn’t change because it wouldn’t cross an equals sign. In this case, we would have -5 + 2x = 13.

If you use these Algebra 1 mental shortcuts wisely, then you should have fewer problems and make fewer mistakes when you’re rearranging the terms inside of expressions and equations.