To solve the inequality [tex]\(-1.7 \leq x < 1\)[/tex] and find all the integer values that [tex]\(x\)[/tex] can take, let’s break it down step by step:
1. Identify the bounds of the inequality:
- The lower bound is [tex]\(-1.7\)[/tex]
- The upper bound is [tex]\(1\)[/tex]
2. Determine the range of integers within these bounds:
- An integer is a whole number, so we need to find whole numbers that lie within [tex]\(-1.7\)[/tex] and [tex]\(1\)[/tex].
3. Consider the lower bound [tex]\(-1.7\)[/tex]:
- Since [tex]\(-1.7\)[/tex] is not an integer, we look at the next integer greater than [tex]\(-1.7\)[/tex], which is [tex]\(-1\)[/tex].
- [tex]\(\-1\)[/tex] is greater than [tex]\(-1.7\)[/tex] and is within the allowed range.
4. Consider the upper bound [tex]\(1\)[/tex]:
- The inequality is strict on the upper side, meaning [tex]\(x\)[/tex] must be less than [tex]\(1\)[/tex] but not equal to [tex]\(1\)[/tex].
- The largest integer that is less than [tex]\(1\)[/tex] is [tex]\(0\)[/tex].
5. Collect all integers between [tex]\(-1.7\)[/tex] (inclusive) and [tex]\(1\)[/tex] (exclusive):
- The integers within the interval [tex]\(-1\)[/tex] to [tex]\(1\)[/tex] (exclusive) are [tex]\(-1\)[/tex] and [tex]\(0\)[/tex].
6. Final conclusion:
- The integer values that satisfy the inequality [tex]\(-1.7 \leq x < 1\)[/tex] are [tex]\(-1\)[/tex] and [tex]\(0\)[/tex].
Therefore, the integer values that [tex]\(x\)[/tex] can take are [tex]\(-1\)[/tex] and [tex]\(0\)[/tex].
