1 Answer

Migdoel · Answer 1 · 2021-06-25T08:22:40+0000

Given:

The inequality is
$y \leq |3x - 6| + 2$ .

Alisha solved the given inequality and got

$y \leq 3x -4$ for
$x \geq 2$ and
$y \leq -3x - 4$ for
x < 2 .

To find:

The Alisha's error, and the correct answer.

Solution:

We have,

$y\leq |3x-6|+2$

For
$x \geq 2, |3x-6|=3x-6$ . So,

$y\leq 3x-6+2$

$y\leq 3x-4$

For
x < 2, |3x-6|=-(3x-6) . So,

$y\leq -(3x-6)+2$

$y\leq -3x+6+2$

$y\leq -3x+8$

Alisha's second inequality is wrong because she did not distribute the negative with 6.

Therefore, the correct answer is

$y \leq 3x -4$ for
$x \geq 2$ and
$y \leq -3x +8$ for
x < 2 .

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