Question

3<7 - 4x < 15-12 < 2(x + 3) <4​

Answer 1

1) (-2 < x, x < 1)

2) (-9 < x, x < -1)

Answer 2

To solve the inequality 3 < 7 - 4x < 15 - 12 < 2(x + 3) < 4, you should break it down into individual inequalities and solve each one separately. Here's the step-by-step solution:

1. Start with 3 < 7 - 4x:

   Subtract 7 from both sides:

   -4 < -4x

   Now, divide both sides by -4. Since you're dividing by a negative number, you need to reverse the inequality sign:

   1 > x

2. Next, move on to 7 - 4x < 15 - 12:

   Simplify both sides:

   7 - 4x < 3

   Subtract 7 from both sides:

   -4x < -4

   Divide both sides by -4 (and reverse the inequality sign):

   x > 1

3. Now, solve 15 - 12 < 2(x + 3) < 4:

   First, simplify the middle part:

   15 - 12 < 2(x + 3)

   3 < 2(x + 3)

   Divide both sides by 2:

   3/2 < x + 3

   Subtract 3 from both sides:

   -3/2 < x

   Now, for the right part:

   2(x + 3) < 4

   Divide both sides by 2:

   x + 3 < 2

   Subtract 3 from both sides:

   x < -1

So, the solution to the inequality 3 < 7 - 4x < 15 - 12 < 2(x + 3) < 4 is:

-1 < x < 1