Find the interval satisfying the inequality       

 `4 - 1/2 x >= -7 + 1/4 x`

Solution:

To find the interval satisfying the inequality 4 - (1/2)x ≥ -7 + (1/4)x, we can solve it step by step.

First, let's simplify the equation by combining like terms:

4 - (1/2)x ≥ -7 + (1/4)x

Multiplying both sides of the inequality by 4 to eliminate the fractions:

16 - 2x ≥ -28 + x

Next, let's isolate the variable on one side of the inequality. Subtracting x from both sides:

16 - 2x - x ≥ -28

16 - 3x ≥ -28

Now, let's isolate the variable further by subtracting 16 from both sides:

-3x ≥ -28 - 16

-3x ≥ -44

To solve for x, we need to divide both sides of the inequality by -3. However, since we are dividing by a negative number, the inequality sign will flip:

x ≤ (-44) / (-3)

x ≤ 44/3

The solution to the inequality is x ≤ 44/3. In interval notation, this can be written as (-∞, 44/3] or (-∞, 14.67].