Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π. (enter your answers as a comma-separated list.)

All the possible values of x such that are: and this can be evaluated by using the trignometry properties.

Given :

All possible values of x can be determine by using trignometry properties. According to trignometry properties:

If than  .

Now put the values of which is 2x and which is x in above expression.

But the above solution is the general solution, the question ask the value of x between 0 and .

Therefore, at k = 0:

at k = 1:

at k = 2:

So, all the possible values of x such that are:

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an altitude of 15,000 feet

step-by-step explanation:

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.