Find the integral values which satisfy the inequality 3x+4≤4x+6<2x+18

Answer 1

Starting with the left inequality, 3x + 4 ≤ 4x + 6, we can subtract 3x from both sides to get:

4 ≤ x + 6.

Then, subtracting 6 from each side gives:

-2 ≤ x.

Now, considering the right inequality, 4x + 6 < 2x + 18, we can subtract 2x from both sides to get:

2x + 6 < 18.

Subtracting 6 from each side gives:

2x < 12.

Dividing both sides by 2 gives:

x < 6.

Therefore, the solution to the inequality 3x + 4 ≤ 4x + 6 < 2x + 18 is -2 ≤ x < 6. The integral values which satisfy this inequality are -2, -1, 0, 1, 2, 3, 4, 5.