Question

What are the solutions to the equation (2x – 5)(3x – 1) = 0?

Answer 1

Answer: $x=\frac{5}{2}, x=\frac{1}{3}$

Explanation:

The equation is:

$(2x-5)(3x-1)=0$

The term on the left consists of a product of two different factors: therefore, this product can be zero if either the first term (2x-5) or the second term (3x-1) is equal to zero.

This means that we can solve separately for the two terms:

$2x-5=0\\3x-1=0$

Solving the first equation:

$2x-5=0\\2x=5\\x=\frac{5}{2}$

Solving the second equation:

$3x-1=0\\3x=1\\x=\frac{1}{3}$

Answer 2

Answer:

$\textbf{The solution of the given equation are : }\frac{5}{2}\textbf{ and }\frac{1}{3}$

Step-by-step explanation:

The equation is given to be : (2x – 5)(3x – 1) = 0

We need to find the values of x such that the value of the equation is 0 and those corresponding values of x will be our required solution of the given equation.

Now, the product of two factors is given to be 0

⇒ Either of the two factors is equal to 0

So, first taking 2x - 5 = 0 and finding the value of x

⇒ 2x = 5

$\implies\bf x=\frac{5}{2}$

Now, taking the second factor equal to 0 and finding the other value of x

⇒ 3x - 1 = 0

⇒ 3x = 1

$\implies\bf x = \frac{1}{3}$

So, we get :

$\bf x =\frac{5}{2}\textbf{ and }x=\frac{1}{3}$

Hence, these two values of x are the required solution of the given equation

$\textbf{Hence, the solution of the given equation are : }\frac{5}{2}\textbf{ and }\frac{1}{3}$