Answer:
- 8 < x < 0
Interval notation: (-8, 0)
Step-by-step Explanation:
Given the compound inequality statement, - 7 < -(x + 7) < 1 :
Solve the compound inequality in groups:
- 7 < -(x + 7) and -(x + 7) < 1
- 7 < -(x + 7)
Switch sides to make it easier to solve:
-(x + 7) > - 7
Using the multiplication property of inequality where it states that multiplying each side of an inequality with a negative number reverses the direction of the inequality symbol.
Multiply both sides by -1 to eliminate the negative sign, and reverse the inequality:
(-1 ) -(x + 7) > (- 7) (-1 )
x + 7 < 7
Then, subtract 7 from both sides to isolate y:
x + 7 - 7 < 7 - 7
x < 0
Next, we'll work on the other group:
-(x + 7) < 1
Multiply both sides by -1 to eliminate the negative sign, and reverse the inequality:
(-1 ) -(x + 7) > 1 (-1 )
x + 7 > - 1
Subtract 7 from both sides:
x + 7 - 7 > - 1 - 7
x > -8
Therefore, the correct answer is: - 8 < x < 0, or in interval notation: (-8, 0).
