Question

What is the solution set to the equation (2x−4)(4x−5)=0

Answer 1

First, distribute the parenthesis:
(2x - 4) (4x - 5) = 8x - 20
 \___\_/___/
       |       |
2x * 4x, 4 * 5
Then you add 20 to both sides
8x - 20 = 0
      +20 +20
8x = 20
Then you divide both sides by 8
$\frac{8x = 20}{8}$
x = 2.5

I think I did that right... I don't quite remember what a solution set is

Answer 2

Answer:

$\left \{ 2,\frac{5}{4} \right \}$

Step-by-step explanation:

We know that for equation of type $(x-a)(x-b)=0$, solutions are $x=a\,,\,x=b$ as both points x = a and x = b satisfy the equation (x-a)(x-b)=0

Given : equation (2x−4)(4x−5)=0

To find  : Solution set of this equation .

Solution :

On dividing this equation by 2 and 4, we get

$\left ( \frac{2x-4}{2} \right )\left ( \frac{4x-5}{4} \right )=0\\\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0$

On comparing equation $\left ( x-2 \right )\left ( x-\frac{5}{4} \right )=0$ with $\left ( x-a \right )\left ( x-b \right )=0$, we get $a=2\,,\,b=\frac{5}{4}$

Therefore, solution set is $\left \{ 2,\frac{5}{4} \right \}$