We are given statement: x differs from minus7 by more than 3.
Soltution: Differ or difference represents subtraction operation.
So, " x differs from minus7" represents " -7 -x ".
Now, for "more than" pharse we would put more than inequality sign " > " .
We also need to involve absolute sign.
So, final expression would be
|-7 -x| > 6.
Now, let us solve this for x.
In order to solve it for x, we need to split it into two inequalities by removing absolute sign | |.
So, we get two inequalities
-7-x > 6 or -7-x< - 6.
Solving -7-x > 6.
Adding 7 on both sides, we get
-7+7-x > 6+7
-x > 13.
Dividing both sides by -1.
We get x< -13 ( Sign of inequality get filp when we divide by a negative number)
Solving -7-x < - 6.
Adding 7 on both sides, we get
-7+7-x < -6+7
-x < 1
Dividing both sides by -1
x>-1.
So , our final answer would be x>-1 or x< -13 .
