1. solve the following inequality to find a range of values for x : -18 < x -7 < -6
2. solve the following inequality to find a range of values for x : -96 < -12x < -12
For the first one just add 7 to each part of the inequality.
that will leave x alone in the middle.
For the second one, this gets a little tricky.
You have to divide each part of the inequality by -12. Whenever you multiply or divide and inequality by a negative number you have to change the direction of the inequalities.
8> x > -1
Saying 8 is greater than 8 and x is greater than -1
is the same thing as saying -1 is less than x and x is less than 8.
we can right the answer in the normal format.
-1 <x <8
thank you, Dr. Jane
Can i ask two more question
1. solve the following inequality to find a range of values for x: -11 < -4-x < -7
2. solve the following inequality to find a range of values for x: -25 < -x < -10
1. solve the following inequality to find a range of values for x: -11 < -4-x < -7
2. solve the following inequality to find a range of values for x: -25 < -x < -10
1. you have to add 4 to each part of the inequality and then divide by -4. That will cause the same reversal as above. Be careful with that final answer.
2. Multiply each part by -1
25>x>10
You have to turn this around for your final answer.. Like we did above.
1. To solve the inequality -18 < x -7 < -6, we need to isolate the variable x.
First, let's solve the left inequality: -18 < x - 7.
Add 7 to both sides of the inequality: -18 + 7 < x.
Simplify: -11 < x.
Now, let's solve the right inequality: x - 7 < -6.
Add 7 to both sides of the inequality: x < -6 + 7.
Simplify: x < 1.
Therefore, the solution to the inequality -18 < x - 7 < -6 is -11 < x < 1.
2. To solve the inequality -96 < -12x < -12, we need to isolate the variable x.
First, let's solve the left inequality: -96 < -12x.
Divide both sides of the inequality by -12.
Remember, when dividing or multiplying an inequality by a negative number, the direction of the inequality symbol must be flipped.
Divide both sides of the inequality by -12, and flip the direction of the inequality: -96/(-12) > x.
Simplify: 8 > x.
Now, let's solve the right inequality: -12x < -12.
Divide both sides of the inequality by -12.
Divide both sides of the inequality by -12, and remember to flip the direction of the inequality: -12/(-12) > x.
Simplify: 1 > x.
Therefore, the solution to the inequality -96 < -12x < -12 is 8 > x > 1.