Question

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

Answer 1

x = - 5 or x = - 1

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

Answer 2

There are 2 roots: -1 and -5.

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