What are the solutions to the inequality (4x-3)(2x-1) greater than or equal to 0

3/4 and 1/2

Step-by-step explanation:

(4x-3)(2x-1) ≥ 0

If the product of 2 numbers is zero, the one of the numbers must be equal to zero.

(4x-3)(2x-1) ≥ 0

(4x-3) ≥ 0               or          (2x-1) ≥ 0

4x ≥ 0+3                               2x ≥ 0+1

4x ≥ 3                                  2x ≥ 1

x ≥ 3/4                                  x ≥ 1/2

Solutions are x ≥ 3/4 and x ≥ 1/2.

Step-by-step explanation:

In the given question an inequality has been given and we have to find out the solutions.

First we write down the inequality as

(4x-3)(2x-1) ≥ 0

From this inequality we can say that there are two solutions.

Therefore the factor 4x-3 ≥ 0 ⇒ 4x ≥ 3

⇒ x ≥ 3/4

Now 2x-1 ≥ 0

⇒ 2x ≥ 1

⇒ x ≥ 1/2

means this inequality has the two sets of the solutions.

One is all the positive numbers greater than equal to 3/4 and all the positive numbers greater than equal to 1/2.

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct