How to solve 4|-6x+6|+-3=93?

otium9ag

otium9ag

Answered question

2023-01-30

How to solve 4 | - 6 x + 6 | + - 3 = 93 ?

Answer & Explanation

Scarlet Barrett

Scarlet Barrett

Beginner2023-01-31Added 6 answers

The initial step in tackling an absolute value equation is to separate the absolute value to one side of the equation.
4 | - 6 x + 6 | + - 3 + 3 = 93 + 3
4 | - 6 x + 6 | + 0 = 96
4 | - 6 x + 6 | = 96
4 | - 6 x + 6 | 4 = 96 4
4 | - 6 x + 6 | 4 = 96 4
| - 6 x + 6 | = 24
We must consider both cases for the term within the absolute value, since the absolute value converts both negative and positive numbers to a negative result 24 and - 24 :
- 6 x + 6 = 24
- 6 x + 6 - 6 = 24 - 6
- 6 x + 0 = 18
- 6 x = 18
- 6 x - 6 = 18 - 6
- 6 x - 6 = - 3
x = - 3
and
- 6 x + 6 = - 24
- 6 x + 6 - 6 = - 24 - 6
- 6 x + 0 = - 30
- 6 x = - 30
- 6 x - 6 = - 30 - 6
- 6 x - 6 = 5
x = 5

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