# by algebraic method.?

4x2 - 4x - 3 ≤ 0

Now solve the equation using factor method.

4x2 - 6x + 2x - 3 ≤ 0

2x(2x - 3) + 1(2x - 3) ≤ 0

Take out common factors.

(2x + 1)(2x - 3) ≤ 0

2x + 1 ≤ 0 or 2x - 3 ≤ 0

2x + 1 ≤ 0

Subtract 1 from each side.

2x  ≤ -1.

Divide each side by 2.

x  ≤ -1/2

And 2x - 3 ≤ 0

2x ≤ 3

Divide each side by 2.

x ≤ 3/2.

Therefore x ≤ -1/2 or x ≤ 3/2.

Graph the solution set on a number line.

The solution of the inequality 4x2 - 4x - 3 ≤ 0 is {x | -1/2 ≤ x ≤ 3/2}.

The inequality is 4x2 - 4x - 3 ≤ 0

Related equation is 4x2 - 4x - 3 = 0

By factor by grouping.

4x2 - 6x + 2x - 3 = 0

2x(2x - 3) + 1(2x - 3) = 0

Factor : (2x - 3)(2x + 1) = 0

4x2 - 4x - 3 = (2x - 3)(2x + 1)

(2x - 3)(2x + 1) ≤ 0

Now, there are two ways this product could be less than or equals to zero.One factor must be negative and one must be positive.

First situation: 2x - 3 ≤ 0 and 2x + 1 ≥ 0

2x ≤ 3 and 2x ≥ - 1

x ≤ 3/2 and x ≥ - 1/2.

Second situation:

2x - 3 ≥ 0 and 2x + 1 ≤ 0

2x  ≥ 3 and 2x ≤ - 1

x  ≥ 3/2 and x ≤ - 1/2.

There are NO values for which this situation is true.

The solution set is {x | -1/2 ≤ x ≤ 3/2}.