Question

Solve, write your answer in interval notation and graph the solution set.

14c. |2x-1|+7 greater than or equal to 1

14d. |5x+3| less than or equal to -1

Answer 1

Solve, write your answer in interval notation and graph the solution set.

14c. $|2x - 1| + 7$ greater than or equal to 1

14d. $|5x + 3|$ less than or equal to -1

Solution:

14c. $|2x - 1| + 7 \geq 1$

$$|2x - 1| \geq -6$$

It is known, that $|a| \geq 0$, so, obviously, $|2x - 1| \geq 0 \Rightarrow |2x - 1| \geq -6 \ \forall x$

Answer: $(-\infty; +\infty)$

14d. $|5x + 3| \leq -1$

It is known, that $|a| \geq 0$, so it can't be $\leq 0$, or $\leq -1$. Obviously, our equation has no solution.

Answer: empty set (no solutions).