### Home > INT2 > Chapter 5 > Lesson 5.1.5 > Problem5-53

5-53.

What values of $x$ will make the following equations true?

1. $| x - 4 | = 3$

$x - 4 = 3$ or $x - 4 = -3$

$x = 1$ or $7$

1. $| x - 4 |− 3 = 0$

Add $3$ to both sides.
This problem should look familiar now.

1. $| x - 4 |= -3$

Can the absolute value of anything ever equal a negative number?

1. $(x − 4)^2 = 9$

Take the square root of both sides. You should now have two equations,
$x - 4 = 3$ and $x - 4 = -3$
This looks a lot like part (a).

1. $(x − 4)^2 − 9 = 0$

Add $9$ to both sides. Now follow the same steps as in part (d).

1. $(x - 4)^2 = -9$

Can you square any real number and get a negative result?