Informal Algebra Suppose we are asked to solve for x in the following equation: x + 3 = 8 In other words, we are being asked for a number such that when we add 3 to that number we get 8. It is not too hard to see that 5 + 3 = 8, so that x = 5. I call the technique above solving this equation informally. In other words, when we solve algebraic equations informally we are solving for the variable very quickly in our heads. I sometimes call this performing “mental math.” Algebra The Formal Way We can also solve for x formally by subtracting 3 from each side of the equation: x + 3 = 8 -3 -3 x = 5 In other words, when we solve an algebraic equation formally we are writing out all the steps – just as we would do it on a test in school. To save time on the SAT you should practice solving equations informally as much as possible. And although informal skills should take precedence during your SAT prep, you should also practice solving equations formally – this will increase your mathematical skill level. Another Example Let’s try another one: 5x = 30 Informally, 5 times 6 is 30, so we see that x = 6. Formally, we can divide each side of the equation by 5: 5x = 30 5 5 x = 6 A Harder Example Now let’s get a little harder: 5x + 3 = 48 We can still do this informally. First let’s figure out what number plus 3 is 48. Well, 45 plus 3 is 48. So 5x is 45. So x must be 9. Here is the formal solution: 5x + 3 = 48 -3 -3 5x = 45 5 5 x = 9 Exercise Try this one on your own: 3x + 4 = 31 And feel free to post your explanations in the comments. College Board Question In the following video I solve Question 1 from Test 1, Section 3 in the College Board’s Official Study Guide using the methods from this article. Get 800 Test Prep Books If you like the information in this article, you may want to check out the Get 800 collection of test prep books. Please share this information with your Facebook friends: I’ll see you next week… Comments comments