SOLVE ABSOLUTE VALUE EQUATIONS

To solve any absolute value function, it has to be in the form of

|x + a| = k

Here, a and k are real numbers. And there should be only absolute part on the left side.

Let us consider the absolute value equation given below.

|2x + 3| = 5

The following steps will be useful to solve absolute value equations.

Step 1 :

Get rid of absolute sign and divide it into two branches.

Step 2 :

For the first branch, take the sign as it is on the right side.

Step 3 :

For the second branch, change the sign on the right side.

Step 4 :

Then solve both the branches.

Example 1 :

Solve for m :

|6m|  =  42

Solution :

Example 2 :

Solve for x :

|6x|  =  30

Solution :

Example 3 :

Solve for k :

|k - 10|  =  3

Solution :

Example 4 :

Solve for x :

|x/7|  =  3

Solution :

Example 5 :

Solve for a :

|a - 5|/8  =  5

Solution :

|a - 5|/8  =  5

Multiply each side by 8. 

|a - 5|  =  40

Example 6 :

Solve for p :

-3|p|  =  -12

Solution :

-3|p|  =  -12

Divide each side by -3. 

|p|  =  4

Example 7 :

Solve for m :

|7m| + 3  = 73

Solution :

|7m| + 3  = 73

Subtract 3 from each side. 

|7m|  =  70

Example 8 :

Solve for v :

-10|v + 2|  =  -70

Solution :

-10|v + 2|  =  -70

Divide each side by -10. 

|v + 2|  =  7

Example 9 :

Solve for v :

|-9 + v|/8  =  3

Solution :

|-9 + v|/8  =  3

Multiply each side by 8. 

|-9 + v|  =  24

Example 10 :

Solve for n :

|n| + 1  =  2

Solution :

|n| + 1 = 2

Subtract 1 on both sides. 

|n|  =  1

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