Chapter A.9, Problem 128AYU

To determine

To find: Make up an inequality that has no solution. Make up one that has exactly one solution.

Answer to Problem 128AYU

$|2x + 3| + 9 \le 7$

Isolate the absolute value by subtracting 9 from both sides of the inequality.

The absolute value of a quantity can never be a negative number, so there is no solution to the inequality.

$x^2 + 1 < -5$ has no real solution

Subtract $-1$ on both sides we get $x^2 < -6$, the square value never be negative, so there is no solution to the inequality.

$x^2 \le 0$ has exactly one solution. The only solution for this is $x = 0$. (Unless $x$ is complex.)

Explanation of Solution

$|2x + 3| + 9 \le 7$

Isolate the absolute value by subtracting 9 from both sides of the inequality.

The absolute value of a quantity can never be a negative number, so there is no solution to the inequality.

$x^2 + 1 < -5$ has no real solution

Subtract $-1$ on both sides we get $x^2 < -6$, the square value never be negative, so there is no solution to the inequality.

$x^2 \le 0$ has exactly one solution. The only solution for this is $x = 0$. (Unless $x$ is complex.)