Solve this equation?

Question

-3 |6n-2| +5=8

Answer 1

Absolute Value Equations : For any real numbers a and b, where b ≥ 0, if  | a |  = b, then a = b or - a = b. This second case is often written as a = - b.

The absolute equation is - 3 | 6n - 1 | + 5 = 8.

Subtract 5 from each side.

- 3 | 6n - 1 | + 5 - 5 = 8 - 5

- 3 | 6n - 1 | = 3

Divide each side by negative 3.

[ - 3 | 6n - 1 | ] / [ - 3 ] = 3 / (- 3).

| 6n - 1 | = - 1.

Because the absolute value of a number is always positive or zero, an equation like | 6n - 1 | = - 1 is never true. Thus, it has no solution. The solution set for this type of equation is the empty set.