Math 1 · Lesson 4 · part 2 of 4
Step 1, before you solve anything: rewrite
Every equation starts with the same move.
Step 1, before you solve anything: rewrite
Every equation starts with the same move. Do both parts, every time, before you touch anything else.
- AGet rid of subtraction and divisionTurn every subtraction into adding the opposite (the additive inverse), and every division into multiplying by the reciprocal (the multiplicative inverse). Now the whole equation is only addition and multiplication.
WhySubtraction and division do not follow the properties of algebra (Lesson 2). They do not commute (5 − 2 is not 2 − 5) and they do not associate, so the rules you learned in Lesson 2 are not written for them. Addition and multiplication pass every test. Once everything is + and ×, you never have to stop and wonder whether a move is allowed.
- BWrite the invisible 1sThe coefficient is the number on the variable: it means the variable is multiplied by that number, so 3x is 3 times x. A lonely x is 1x (the coefficient is 1), and −x is (−1)x. Write them in.
WhyWe usually do not write the 1, and anything algebra leaves you to do in your head is one of the top causes of mistakes. 5x − x is 4x, not 5, and the only reason people get 5 is the 1 they never wrote down.
In the practice problems, the Step 1 rewrite is shown in this color.