Question

-7 < -(x+7) < 1

Answer 1

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).

Answer 2

Answer:

Move all terms not containing x from the center section of the inequality.

Inequality Form:

−8<x<0

Interval Notation:

(−8,0)

Step-by-step explanation: