Question

Solve a combined inequality that is a conjunction of two linear equalities.

1.) solve for n. -1<9+n<17

2.) solve for x. -2<8x-12<_36

Answer 1

1. -10 < n < 8
2. 5/4 < x ≤ 6

Explanation:

1. Subtract 9:

-10 < n < 8

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2. Add 12, then divide by 8:

10 < 8x ≤ 48

10/8 < x ≤ 6

5/4 < x ≤ 6 . . . . . with the fraction reduced

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The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...

-1 -9 < 9 +n -9 < 17 -9

This simplifies to the inequality we show above:

-10 < n < 8