How do you solve the inequality 2| x -5| > 32?

Jun 11, 2018

Solving an inequality involves finding all the possible values of x that satisfy the equation; in this example $x > 21$ and $x < - 11$

Explanation:

To solve any modulus equation, you need to do two separate calculations - one where the bit in the modulus is positive, and one where it is negative. Hence, you will always get two solutions for any (linear) modulus function.

Calculation 1 (positive):
$2 \left(x - 5\right) > 32$
$2 x - 10 > 32$
$2 x > 42$
$x > 21$

Calculation 2 (negative):
$- 2 \left(x - 5\right) > 32$
$- 2 x + 10 > 32$
$- 2 x > 22$
$- x > 11$
$x < - 11$

Notice that when you change the negative signs, you must also flip the direction of the inequality.

You could also solve this graphically by plotting the modulus graph, but as this is more complex (and presents more opportunities for errors) I always stick to this method for solving.