How do I solve this absolute value inequality? Should I add two to both sides first?
| -3n | - 2 = 4
Not inequality I meant equation.
since |x| =
x if x>=0
-x if x<0
so, either
-3n >= 0 and
(-3n) = 6 so n = -2
or
-3n < 0 and
-(-3n) = 6 so n=2
To solve an absolute value inequality, you'll need to consider two conditions: one for when the expression inside the absolute value is positive, and another for when it is negative. Let's break down the steps to solve the given absolute value inequality: | -3n | - 2 = 4.
Step 1: Isolate the absolute value expression on one side:
| -3n | = 4 + 2
| -3n | = 6
Step 2: Consider the case when the expression inside the absolute value is positive:
-3n = 6
To remove the negative sign in front of the variable, divide both sides by -3:
n = -2
Step 3: Consider the case when the expression inside the absolute value is negative:
-(-3n) = 6
Distribute the negative sign:
3n = 6
Divide both sides by 3:
n = 2
So, the possible solutions for the absolute value inequality are n = -2 and n = 2. Since you're dealing with an absolute value inequality, it's also important to check both solutions to ensure they satisfy the inequality by substituting them back into the original equation.