how to find all real solutions of an equation

Question

|1/2×+4|+8=10

Answer 1

|1/2×+4|+8=10

First subtract 8 from both sides to isolate the absolute value.

 

|1/2×+4|=2

Now remember that the absolute value means that if result is negative, you still take the positive version.  This means you can split this into two equations:

 

1/2x+4=2       or         1/2x+4=-2

 

Now you can solve each of these equations for your two solutions.

Answer 2

The first step is to have only the absolute value on one side and the rest on the other side of the equal sign.

|1/2x + 4| + 8 = 10

|1/2x + 4| = 2

 

Then we know that an absolute value makes a positive value positive and a negative value positive (|5| = 5 and |-5| = 5)

 

So we take the inside of the absolute value (1/2x + 4) and set it equal to the value on the other side of the equation and the negate value.

 

(1/2x + 4) = 2    and (1/2x + 4) = -2

 

Solve each equation to get two real answers.

 

1/2x + 4 = 2

        -4      -4

1/2x = -2

* 2/1      * 2/1

x = -4

 

1/2x + 4 = -2

        -4      -4

1/2x = -6

*2/1    *2/1

x = -12

 

 

Always double check your answer!

|1/2x + 4| + 8 = 10

 

|1/2(-4) + 4| + 8 = 10

|-2 + 4| + 8 =10

|2| + 8 = 10

2 + 8 = 10

 

|1/2(-12) + 4| + 8 = 10

|-6 + 4| + 8 =10

|-2| + 8 = 10

2 + 8 = 10