Solve and write answer in interval notation help!?

Question

Solve 
-4 < 2x + 4 < 10 

Solve 
-3m - 7 < 5 or -3m - 7 > 14 

Answer 1

• The inequality - 4 < 2x + 4 < 10

Subtract 4 from each side of inequality.

- 4 - 4 < 2x + 4 - 4 < 10 - 4

- 8 < 2x < 6

Divide each side by  2.

- 4 < x < 3

Solution {x | - 4 < x < 3}

Solution of - 4 < 2x + 4 < 10 in interval notation (-4, 3).

 

• The inequality - 3m - 7 < 5 or - 3m - 7 > 14

Solve the inequality : - 3m - 7 < 5

Add 7 to each side of inequality.

- 3m  - 7 + 7 < 5 + 7

-3m  < 12

Divide each side by  negative 3 and flip the symbol.

(-3m )/(-3) > 12/(-3)

m  > - 4

Solve the inequality : - 3m  - 7 > 14

Add 7 to each side of inequality.

- 3m - 7 + 7 > 14 + 7

- 3m  > 21

Divide each side by  negative 3 and flip the symbol.

(-3m )/(-3) < 21/(-3)

m  < -7

Soltions are m  > - 4 or m  < - 7

Solution of - 3m - 7 < 5 or - 3m - 7 > 14 in interval notation (-∞, -7)U(-4, ∞).