Question

Solve the inequality 3|2x - 4| > 6 graphically. Write the solution in interval notation

Answer 1

Explanation:

To solve this inequality graphically, we need to find the values of x that make the inequality true. We can start by looking at the absolute value expression on its own.

The absolute value of a number is always non-negative, so we can split the inequality into two cases: when the expression inside the absolute value is positive, and when it is negative.

For the first case, we have:

3|2x - 4| > 6

2x - 4 > 0

x > 2

For the second case, we have:

3|2x - 4| > 6

2x - 4 < 0

x < 2

So, the solution to the inequality is the union of these two cases: x > 2 or x < 2. In interval notation, this is written as (-infinity, 2) U (2, infinity).

Answer 2

(-∞, 1) ∪ (3, ∞)

Explanation:

You want a graphical solution to 3|2x -4| > 6.

Graph

The attached graph is of the expression ...

3|2x -4| -6

This is greater than 0 where x is a solution to the given inequality. It is greater than 0 for x < 1 or for 3 < x. In interval notation, the solution is ...

(-∞, 1) ∪ (3, ∞)