Which of the following represents the solution to the inequality 2 | 5 - 2x | - 3 ≤ 15 a. (-∞,-2) u (7,∞) b. (-∞,1.5) u (7.5,∞) c. [-2,7] d. [1.5,7.5]

[-2,7] is the solution of inequality .

Step-by-step explanation:

Given :  inequality 2 | 5 - 2x | - 3 ≤ 15

To find: solution of inequality.

Solution : We have given that 2 | 5 - 2x | - 3 ≤ 15 .

On adding 3 both sides:

2 | 5 - 2x | - 3+3 ≤ 15 +3

2 | 5 - 2x |  ≤ 18.

ON dividing both side by 2 and simplify

| 5 - 2x |  ≤ 9.

On applying absolute rule,  if | u | ≤ a,a>  then -a ≤ u≤ a

-9≤5 - 2x ≤ 9.

5 - 2x ≤ 9                 ,    5 - 2x ≤ -9.

- 2x ≤ 9-5

- 2x ≤ 4

On dividing by -2

x ≥ -2.

For  5 - 2x ≤ -9.

 - 2x ≤ -9-5

- 2x ≤ -14

On dividing by -2

x ≤ 7

Therefore ,  [-2,7] is the solution of inequality .

C. [-2,7]

Step-by-step explanation:

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step-by-step explanation: