Question

State all integer values of x in the interval−3≤x≤2 that satisfy the following intequality : −4x+6≥13

Answer 1

To find the integer values of x in the interval -3≤x≤2 that satisfy the inequality -4x+6≥13, we can solve it step-by-step:

1. Subtract 6 from both sides of the inequality: -4x+6-6≥13-6.

2. Simplify: -4x≥7.

3. Divide both sides of the inequality by -4. Remember that when we divide an inequality by a negative number, the direction of the inequality sign is reversed: -4x/-4≤7/-4.

4. Simplify: x≤-7/4.

Now, we need to find the integer values of x that satisfy the inequality in the given interval -3≤x≤2.

Since -7/4 is less than -3, it is not within the interval -3≤x≤2. Therefore, there are no integer values of x in the interval -3≤x≤2 that satisfy the inequality -4x+6≥13.