To solve the inequality [tex]\( 15 \geq 22 + x \)[/tex], follow these steps:
1. Subtract 22 from both sides of the inequality:
[tex]\[
15 - 22 \geq x
\][/tex]
2. Simplify the left-hand side:
[tex]\[
-7 \geq x
\][/tex]
3. This inequality means that [tex]\( x \leq -7 \)[/tex].
Based on this solution, we analyze each of the given statements:
1. [tex]\( x \geq -7 \)[/tex]:
- This statement is false because our solution states that [tex]\( x \leq -7 \)[/tex].
2. [tex]\( x \leq -7 \)[/tex]:
- This statement is true as it matches our solution.
3. The graph has a closed circle:
- This statement is true because the inequality includes the value [tex]\(-7\)[/tex], which means the circle at [tex]\(-7\)[/tex] is closed (or filled in).
4. [tex]\(-6\)[/tex] is part of the solution:
- This statement is false because [tex]\(-6\)[/tex] does not satisfy [tex]\( x \leq -7 \)[/tex] (since [tex]\(-6\)[/tex] is greater than [tex]\(-7\)[/tex]).
5. [tex]\(-7\)[/tex] is part of the solution:
- This statement is true because [tex]\(-7\)[/tex] satisfies [tex]\( x \leq -7 \)[/tex].
Therefore, the three true statements about the solution of [tex]\( 15 \geq 22 + x \)[/tex] are:
- [tex]\( x \leq -7 \)[/tex]
- The graph has a closed circle
- [tex]\(-7\)[/tex] is part of the solution
