Final answer:
To solve |(5f-2)/6| > 4, the inequality is split into f > 5.2 and f < 4.4. On a number line, this is represented by two shaded regions, one to the left of 4.4 and one to the right of 5.2, with neither 4.4 nor 5.2 included.
Step-by-step explanation:
To solve the inequality The absolute value of 5f-2/6 > 4, we begin by considering the nature of absolute values. An absolute value inequality like |x| > a, where a is a positive number, is satisfied if x > a or x < -a. Therefore, we split our inequality into two separate cases, one where the expression inside the absolute value is positive, and one where it's negative.
For the positive case, we have (5f - 2)/6 > 4. Multiplying both sides by 6 to clear the fraction gives us 5f - 2 > 24, or 5f > 26, which simplifies to f > 26/5, or f > 5.2.
For the negative case, we have -(5f - 2)/6 > 4. Multiplying both sides by 6 gives us -(5f - 2) > 24, or 2 - 5f > 24, which leads to -5f > 22. Dividing by -5, and remembering to reverse the inequality sign, gives us f < -22/-5, or f < 4.4.
Now we can graph on a number line:: One should draw a number line, marking the points f = 4.4 and f = 5.2. The solution to the original inequality includes all values to the right of 5.2 and to the left of 4.4, so these regions should be shaded or marked in some way to indicate that they are included in the solution set, but the points 4.4 and 5.2 are not included (since our inequality is strict, not 'greater than or equal to'). The graph will show two rays extending from 4.4 (excluding) to negative infinity, and from 5.2 (excluding) to positive infinity.