Answer:
Absolute Value inequalities will have 2 solutions.
x > 10 AND x < 2
Explanation:
The first thing that we need to do to solve this inequality is start isolating the given variable: x
Our first step should be subtracting 3 from both sides:
2 * |x - 6l + 3 > 11
subtract 3 from both sides...
2 * |x - 6l > 8
Now our next step on the way to isolating x should leave us with the absolute value expression by itself. To do this we can divide both sides by 2:
2 * |x - 6l > 8
now divide both sides by positive 2...
|x - 6l > 4
Now for the final step we just need to get x by itself. We can do this one of two ways. First, we can use logic to solve the expression and find x, or we can split the absolute value into two separate expressions and solve for x from there.
Let's split the absolute value into two separate expressions:
(x-6) > 4
AND
-(x-6) > 4 OR (-x+6) >4
We'll replace the absolute value signs with parenthesis for our first solution. And place a negative sign in front of the parenthesis for our second solution.
Now we can isolate x using simple addition and subtraction and solve the inequality.
x - 6 > 4
x > 10
AND
-x + 6 > 4
-x > -2
x < 2
IMPORTANT: Remember that when solving an inequality, you must flip the sign if you divide or multiply by a negative number. We divide -x > -2 by -1 for our second solution, so the > must change to a <.
Now we have our two solutions.
x > 10 AND x < 2
If graphed, make sure to graph dotted lines on x = 2 and x = 10, as this inequality was greater than (>) rather than greater than or equal to (≥).