Math 1 · Lesson 5 · part 2 of 5
The three steps
Same three steps every time, however long the equation gets.
The three steps
Same three steps every time, however long the equation gets. Each one has a property name you can say out loud.
- 1RewriteTurn every subtraction into adding the additive inverse (the opposite), and every written ÷ sign into multiplying by the multiplicative inverse (the reciprocal). Write in every invisible 1: a lonely x is 1x, and −x is (−1)x.
- 2Distribute, then combine like termsHand the outside number to every term inside the parentheses (the distributive property). Then combine the like terms (the terms with the same letter part) with the distributive property run backwards: 5x + 2x = (5 + 2)x = 7x.
- 3x terms one side, plain numbers the otherAdd the opposite of the smaller x term to both sides, then the opposite of the plain number (the addition property of equality). Finish by multiplying both sides by the reciprocal of the coefficient (the multiplication property of equality), so the last line reads x = the answer.
- 4CheckPut your answer back into the original equation, written with plus the opposite. Both sides should match.
A fraction bar is not a written ÷ sign, so Step 1 has nothing to rewrite there. x3 already is the coefficient (the number on the variable) 13 on x.