Question

Let f(x) = 13 - |2x+ 1|. Find all x for which f(x) less than or equal to 14

Answer 1

Answer:

$x \leqslant -1\: or \: x \geqslant - 1$

Step-by-step explanation:

The given function is

$f(x) = 13 - |2x + 1|$

We want to find all values of x for which:

f(x) is greater than or equal to 14.

This implies;

$13 - |2x + 1| \geqslant 14$

Subtract 13 from both sides;

$- |2x + 1| \geqslant 14 - 13$

$|2x + 1| \geqslant - 1$

By definition of the absolute value function,

$- (2x + 1) \geqslant - 1 \: or \: (2x + 1) \geqslant - 1$

Divide through the first inequality and and reverse the inequality sign:

$2x + 1 \leqslant -1 \: or \: 2x + 1 \geqslant - 1$

$2x \leqslant -1 - 1 \: or \: 2x \geqslant - 1 - 1$

$2x \leqslant -2 \: or \: 2x \geqslant - 2$

$x \leqslant -1\: or \: x \geqslant - 1$