Math 1 · Lesson 7 · part 5 of 7
The steps
1 Rewrite Step 1 as always, inside the bars and outside them: subtraction becomes adding the additive...
The steps
- 1RewriteStep 1 as always, inside the bars and outside them: subtraction becomes adding the additive inverse (the opposite), a written ÷ becomes multiplying by the multiplicative inverse (the reciprocal), and the invisible 1s get written in.
- 2Get the bars aloneTreat |inside| as one block. Peel off anything added to it or multiplied on it with the Lesson 6 moves. If you multiply by a negative here, flip the sign now.
- 3Read the sign, pick the wordLess than: between, and. Greater than: outside, or. (And if the number on the right is negative, stop: less than gives no solution, greater than gives every number.)
- 4Set up two problems and solve bothSame inside in each. Solve each one exactly as in Lesson 6, naming the property on every line, and flip in both if a coefficient (the number on the variable) is negative.
- 5Write the answer with its word, graph it, checkAn and-answer is a sandwich, one shaded stretch. An or-answer is two pieces with a gap. Check in the original, with a number from each piece and from each gap.
Why the two problems always have the same insideThe bars only ever hide one thing: the sign of the inside. Between means the inside might be a little negative or a little positive, so you write both. Outside means the inside is very negative or very positive, so you write both. In every case the inside itself is the same expression, and once the bars are off, you are back in Lesson 6.