|3x-11|=x+3
Write both solutions as equations on the same line separated by a comma.

x = 2, x = 7

Step-by-step explanation:

Given

| 3x - 11 | = x + 3

The absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, thus

3x - 11 = x + 3 or - (3x - 11) = x + 3

Solving both equations

3x - 11 = x + 3 ( subtract x from both sides )

2x - 11 = 3 ( add 11 to both sides )

2x = 14 ( divide both sides by 2 )

x = 7

or

- (3x - 11) = x + 3

- 3x + 11 = x + 3 ( subtract x from both sides )

- 4x + 11 = 3 ( subtract 11 from both sides )

- 4x = - 8 ( divide both sides by - 4 )

x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions

x = 7

| 3(7) - 11 | = | 21 - 11 | = | 10 | = 10

right side = 7 + 3 = 10 → both sides are equal thus x = 7 is a solution

x = 2

| 3(2) - 11 | = | 6 - 11 | = | - 5 | = 5

right side = 2 + 3 = 5 → both sides are equal thus x = 2 is a solution

The solutions are x = 2, x = 7

180

step-by-step explanation:

-2 is the right