Solve: 5 | x + 3 | - 25 = - 15

There are 2 roots: - 1 and - 5.

Step-by-step explanation:

5 | x + 3 | - 25 = - 15

Add 25 to both sides.

5|x + 3| = 10

Divide both sides by 5.

|x + 3| = 2

Now, the x + 3 can be positive or negative.

So we have 2 equations:-

x + 3 = 2 and x + 3 = - 2

So x = 2. - 3 = - 1

and x = - 2-3 = - 5

x = - 5 or x = - 1

Step-by-step explanation:

isolate the absolute value expression

add 25 to both sides

5|x + 3| = 10 (divide both sides by 5)

| x + 3 | = 2

the expression inside the bars can be positive or negative, hence

x + 3 = 2 or - (x + 3) = 2

x = 2 - 3 = - 1 or - x - 3 = 2 ⇒ - x = 2 + 3 = 5 ⇒ x = - 5

As a check

substitute these values into the left side and if equal to the right side then they are the solutions

x = - 1 : 5| - 1 + 3| - 25 = 5|2| - 25 = (5 * 2) - 25 = 10 - 25 = - 15 correct

x = - 5 : 5| - 5 + 3| - 25 = 5| - 2| - 25 = (5 * 2) - 25 = - 15 correct

solutions are x = - 1 or x = - 5