Question

Solve the linear equation for x: \[\dfrac{5x}{3}-4=\dfrac{3x}{5}\].

Answer 1

Hint: First write the single degree equation with the left-hand side and the right-hand side. Find the coefficient of variable on both sides of the equation. Subtract the term with a coefficient of variable on the right-hand side. Now similarly find the constant values on both sides of the equation. Subtract the constant value of the left-hand side on both sides of the equation. Now you get an equation with variable terms on the left-hand side and constant terms on the right-hand side. Now find the coefficient term of variable on the left-hand side. Divide with this coefficient on both the sides of the equation. Now you have only the variable with coefficient 1 on the left-hand side and some constant on the right-hand side. So, this constant will be your result.

Complete step-by-step solution -
Linear Polynomials:
If the degree of the polynomial is 1 then they are called linear polynomials. For example $x + 1, x + 2, x + 3$.
Degree of Polynomial:
The highest power of the variable in a polynomial is called its degree. For example \[{{x}^{2}}+4x+2\] has degree of 2, $x + 1$: degree of 1, \[{{x}^{3}}+1\]: degree of 3, 2 is a polynomial of degree 0.
Given expression in terms of x in the question, is written as:
\[\Rightarrow \dfrac{5x}{3}-4=\dfrac{3x}{5}\]
By taking the least common multiple on the left-hand side, we get:
\[\Rightarrow \dfrac{5x-12}{3}=\dfrac{3x}{5}\]
By applying cross multiplication to the above equation, we get it as:
\[\Rightarrow 5\left( 5x-12 \right)=3\left( 3x \right)\]
By removing parentheses that is multiplying 5 inside, we get:
\[\Rightarrow 25x-60=9x\]
By subtracting with 9x on both sides, we get it as:
\[\Rightarrow 25x-9x-60=9x-9x\]
By simplifying the above equation, we get the equation:
\[\Rightarrow 16x-60=0\]
By adding with 60 on both sides, we get is as:
\[\Rightarrow 16x-60+60=0+60\]
By simplifying the above equation, we get the equation as:
\[\Rightarrow 16x=60\]
By dividing with 16 into both sides of the equation, we get it as:
\[\Rightarrow \dfrac{16x}{16}=\dfrac{60}{16}\]
By simplifying the above equation, we get the value of x as:
\[\Rightarrow x=\dfrac{15}{4}\]
The value of x satisfying the given equation is \[\dfrac{15}{4}\].

Note: While removing parentheses students forget to multiply the constant term and write – 12 but it must be – 60 be careful. An alternate method is to keep all the variable terms to the right-hand side and constant to the left-hand side anyways you get the same result. Whenever you apply an operation on the left-hand side, don’t forget to apply the same on the right-hand side if not you may lead to the wrong answer.