Question

Solve the linear equation 0.7x + 0.3x = 0.5x + 6.

Answer 1

Hint: First write the single degree equation with the left-hand side and right-hand side. Find the coefficient of the variable on both sides of the equation. Subtract the term with a coefficient of the 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 the variable on the left-hand side. Divide with this coefficient on both 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 equation in terms of x is given as follows:
\[\Rightarrow 0.7x+0.3x=0.5x+6\]
By writing each of decimals into fractions, we get it as:
\[\Rightarrow \dfrac{7x}{10}+\dfrac{3x}{10}=\dfrac{5x}{10}+6\]
By taking the least common multiple on the right-hand side, we get:
\[\Rightarrow \dfrac{7x+3x}{10}=\dfrac{5x+60}{10}\]
By canceling the denominator on both sides, we get it as:
\[\Rightarrow 7x+3x=5x+60\]
By subtracting with $5x$ on both sides, we get it as:
\[\Rightarrow 7x+3x-5x=60\]
By taking x common on the right-hand side, we get it as:
\[\Rightarrow x\left( 7+3-5 \right)=60\]
By simplifying the term inside the bracket, we get it as:
\[\Rightarrow 5x=60\]
By dividing with 5 into both sides of the equation, we get it as:
\[\Rightarrow x=\dfrac{60}{5}\]
By simplifying the above equation, we get the value of x as 12.
Therefore the value of the satisfying given equation is 12.

Note: After converting into fractions the constant on the left-hand side will be 60. Generally, students forget the 10 in the denominator and write it as 6 which is wrong. The 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.