9|3−8x|=2x+3

Answer 1

To solve the equation 9|3−8x|=2x+3, we can start by isolating the absolute value term:

9|3−8x| = 2x + 3

Divide both sides of the equation by 9:

|3−8x| = (2x + 3)/9

Now, we have two cases to consider:

Case 1: 3−8x ≥ 0

In this case, the absolute value can be removed:

3−8x = (2x + 3)/9

Multiply both sides of the equation by 9 to get rid of the denominator:

27 - 72x = 2x + 3

Combine like terms:

-74x = -24

Divide both sides by -74:

x = -24/-74

x = 12/37

Case 2: 3−8x < 0

In this case, the absolute value term changes sign:

3−8x = -(2x + 3)/9

Multiply both sides of the equation by 9:

27 - 72x = -2x - 3

Combine like terms:

-70x = -30

Divide both sides by -70:

x = -30/-70

x = 3/7

Therefore, the solution to the equation 9|3−8x|=2x+3 is x = 12/37 and x = 3/7.