How do you solve these math problems?

Question

− 3 ≤  1⁄2 · (5 x + 17) < 5?

 

a) [ -4 , -7⁄5)


b) (-23⁄5 , -7⁄5)


c) [-23⁄5 , -12⁄5)


d) [-23⁄5 , -7⁄5)


e) (-23⁄5 , -7⁄5]


f) None of the above.


 x : | x |  =  30

a) x  =  − 30


b) x  =  0 , x  =  30


c) x  =  − 30 , x  =  30


d) x  =  30


e) x  =  − 30 , x  =  0 , x  =  30


f) None of the above.

 

 

 

Answer 1

1) The inequality - 3 ≤ (1/2) (5x + 17) < 5

- 3 (2) ≤ (1/2) (2) (5x + 17) < 5(2)

- 6 ≤ 5x + 17 < 10

- 6 - 17 ≤ 5x + 17 - 17 < 10 - 17

- 23 ≤ 5x < - 7

- 23/5 ≤ 5x/5 < - 7/5

- 23/5 ≤ x < - 7/5

Solution of the inequality in interval notation [- 23/5 , - 7/5).

Option d is correct.

Answer 2

The expression  | x | = 30

From the definition absolute value |x| = a then x = a or x = - a

x = 30 or x = - 30

Option C is correct.