# How do you solve the equation abs(4-x)=7?

Apr 23, 2017

$x = - 3 \mathmr{and} x = 11$

#### Explanation:

The two vertical lines used this way are a special sort of brackets and they signify an 'Absolute' value. That is; whatever is between those lines is always considered as positive

So if the answer is positive 7 then what is inside those special brackets can only end up as two values. These are $\pm 7$ in that:

$| \pm 7 | = + 7$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the case $4 - x = - 7$

Multiply both sides by (-1) $\to$ changes $- x$ to $+ x$

$- 4 + x = + 7$

Add 4 to both sides $\to$ get rid of the -4 on the left

$- 4 + 4 + x = 4 + 7$

$0 + x = + 11$

So one value is $x = 11$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the case $4 - x = + 7$

Multiply by (-1)

$- 4 + x = - 7$

So the other value is $x = - 3$