Math 1 · Lesson 7 · part 3 of 7
Less than means between: the word is and
Say |inside| < 5.
Less than means between: the word is and
Say |inside| < 5. The inside is closer to zero than 5. On the number line, that is everything between −5 and 5. To be there, the inside has to be bigger than −5 and smaller than 5, both at the same time. So one absolute value sentence becomes two sentences joined by and:
−5 < insidethe inside is to the right of −5
and
inside < 5the inside is to the left of 5
Because both must hold, the answer is one connected stretch, and it can be written as a sandwich: −5 < inside < 5. Read the sandwich from the middle out: the inside is bigger than the left number and smaller than the right one.