How do you graph and solve #abs(3x-7 ) > -1#?

Divide the solution into two parts: a. (3x - 7) > - 1 3x > 6 x > 3 b. -(3x - 7) > - 1 3x + 7 > - 1 3x > - 8 x < 8/3 Plot the results on-line:

========= 0 ====== 8/3--------- 3 =============–

To graph and solve the inequality |3x - 7| > -1:

1. Recognize that absolute values are always non-negative, so the absolute value of any expression is greater than or equal to zero.
2. Since -1 is less than zero, the absolute value of any expression will always be greater than -1. Therefore, the inequality |3x - 7| > -1 is always true for any value of x.
3. The solution set for this inequality is all real numbers.

To graph it:

• Draw a number line.
• Recognize that the inequality holds true for all real numbers.
• Therefore, shade the entire number line.
• Indicate that the solution set is all real numbers.

There is no need to solve the inequality further since it holds true for all real numbers.