# How do you graph and solve #| 3x-12 |>0#?

By signing up, you agree to our Terms of Service and Privacy Policy

To graph and solve the inequality |3x - 12| > 0, we first note that the absolute value of any real number is always non-negative, and it equals zero only when the number itself is zero. Therefore, the absolute value of 3x - 12 is greater than zero for any value of x except when 3x - 12 equals zero.

To find the values of x where 3x - 12 equals zero, we solve the equation 3x - 12 = 0. Solving for x, we get x = 4.

So, the inequality |3x - 12| > 0 holds for all real numbers except x = 4.

To graph this inequality on a number line, we mark an open circle at x = 4 to indicate that it is not included in the solution set. Then, we shade the region to the left and right of x = 4 to represent all real numbers except x = 4.

In interval notation, the solution to the inequality is (-∞, 4) U (4, ∞).

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7