Question

Solve and show all work: |2x + 3| - 6 = 11

Answer 1

Step 1: Add 6 to both sides.

|

2

x

+

3

|

−

6

+

6

=

11

+

6

|

2

x

+

3

|

=

17

Step 2: Solve Absolute Value.

|

2

x

+

3

|

=

17

We know either

2

x

+

3

=

17

or

2

x

+

3

=

−

17

2

x

+

3

=

17

(Possibility 1)

2

x

+

3

−

3

=

17

−

3

(Subtract 3 from both sides)

2

x

=

14

2

x

2

=

14

2

(Divide both sides by 2)

x

=

7

2

x

+

3

=

−

17

(Possibility 2)

2

x

+

3

−

3

=

−

17

−

3

(Subtract 3 from both sides)

2

x

=

−

20

2

x

2

=

−

20

2

(Divide both sides by 2)

x

=

−

10

Answer:

x

=

7

or

x

=

−

10

Answer 2

Answer:

The two solutions are {-10, 7}

Step-by-step explanation:

Add 6 to both sides to simplify this equation:

|2x + 3| - 6 + 6 = 11 + 6, or

|2x + 3|  =  17

This is an absolute value equation.  It actually has two parts:

The first is 2x + 3 = 17, which simplifies to 2x = 14.  Then x = 7.

The other one is -(2x + 3) = 17.  This simplifies to -2x - 3 = 17,

or -2x = 20.  Then x -10.

The two solutions are {-10, 7}