Question

3 |d + 1 |-7>= -1
I don’t know if it’s no solution or not

Answer 1

Answer:
`d \ge 1 \ \text{ or } \ d \le -3\\\\`

Both parts are needed to form the full solution set.

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Work Shown:

`3|d+1|-7 \ge -1\\\\3|d+1| \ge 6\\\\|d+1| \ge 2\\\\d+1 \ge 2 \ \text{ or } \ d+1 \le -2\\\\d \ge 1 \ \text{ or } \ d \le -3\\\\`

In the second step, I added 7 to both sides. In the third step, I divided both sides by 3. Afterward, I used the rule that
`|x| \ge k` breaks down into
`x \ge k \ \text{ or } \ x \le -k` for some positive value k. The last thing to do is to subtract 1 from both sides to fully isolate d.