# math

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solve the absolute value problem : 3x+|4x+5|=10

• math -

In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign.

So, for example, the absolute value of 3 is 3, and the absolute value of
-3 is also 3.

In this case:

| 4 x + 5 | = 4 x + 5

OR

| 4 x + 5 | = - ( 4 x + 5 ) = - 4 x - 5

Equation:

3 x + | 4 x + 5 | = 10

has two solutions.

1.)

3 x + 4 x + 5 = 10

7 x = 10 - 5

7 x = 5 Divide both sides with 7

x = 5 / 7

2.)

3 x - ( 4 x + 5 ) = 10

3 x - 4 x - 5 = 10

- x = 10 + 5

- x = 15 Multiply both sides with - 1

x = - 15

• math -

| 4 x + 5 | = 4 x + 5

| - ( 4 x + 5 ) | = | - 4 x - 5 | = | 4 x + 5 |

• math -

More direct way:

3x+|4x+5|=10
|4x+5| = 10-3x
4x+5 = 10-3x OR -4x-5 = 10-3x
7x = 5 OR -x = 15

x = 5/7 OR x = -15

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