Express the fact that x differs from minus7 by more than 3 as an inequality involving absolute value. solve for x.

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 .

c) yes, because of asa or aas