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

Question

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

Kennedy Adams · Accepted Answer

#x > 4 or x < 4# #|3x - 12| > 0# We need to solve the absolute value We know either #3x - 12 > 0 or 3x - 12 < - 0# So, we gonna solve the first one or the first possibility #3x - 12 > 0# #3x > 0 + 12# #3x > 12# Divide both sides by 3 #(3x)/3 > 12/3# #x > 4# Now let solve the second one or the second possibility #3x - 12 < - 0# #3x < -0 + 12# #3x < 12# Divide both sides by 3 #(3x)/3 < 12/3# #x < 4# Thus, Our final answer is : #x > 4 or x < 4# graph{|3x - 12| > 0 [-10, 10, -5, 5]}

Hazel Anglin · Answer

undefined 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, ∞).

How do you graph and solve #| 3x-12 |&gt;0#?

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