Question

If we have an expression as \[\dfrac{3y+4}{2-6y}=\dfrac{-2}{5}\], then \[y\] is?

Answer 1

Hint: We are given an equation with one variable. Since the equation consists of fractions in both LHS and RHS, we can cross multiply them and then equate it with a variable at one end and the constant on the known terms on the other end. In this way we can obtain the value of \[y\].

Complete step-by-step solution:
Let us know more about polynomial equations in one variable. A polynomial expression with an equal symbol is called a polynomial equation. Polynomial expression with a single term is known as monomial, with two terms is known as binomial, with three terms is known as trinomial, and with 4 or more than 4 terms are known as multinomial. These polynomials are further classified into linear, quadratic, cubic on the basis of the degree of the polynomial.
Now let us find out the value of \[y\]
\[\dfrac{3y+4}{2-6y}=\dfrac{-2}{5}\]
On cross multiplying both the terms, we get
\[\begin{align}
  & \Rightarrow \dfrac{3y+4}{2-6y}=\dfrac{-2}{5} \\
 & \Rightarrow 5\left( 3y+4 \right)=-2\left( 2-6y \right) \\
 & \Rightarrow 15y+20=-4+12y \\
 & \Rightarrow 3y=-24 \\
 & \therefore y=-8 \\
\end{align}\]
\[\therefore \] we have got the value as \[y=-8\].
The graph of this equation would be

Note: The most general rule of a polynomial is that it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. The degree of the polynomial is nothing but the highest power of the term in the expression. The value which solves the expression or equation is known as polynomial value. The given problem can also be solved by trial and error method but this would be more time consuming.