Question

How do you solve \[\dfrac{3}{7}x+5=9\]?

Answer 1

Hint: The given equation is a linear equation in one variable, we know that to solve this equation we need to take the variable terms and constant to different sides. The given equation has only one variable term to its left side. So, to solve this equation we have to take the constants to the right side of the equation and make the coefficient of the variable term one. By doing this, we will get the solution value for x.

Complete step by step solution:
We are given the equation \[\dfrac{3}{7}x+5=9\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[\dfrac{3}{7}x+5=9\]
Subtracting 5 from both sides of the above expression, we get
\[\Rightarrow \dfrac{3}{7}x=4\]
Multiplying \[\dfrac{7}{3}\] to both sides of above equation, we get
\[\Rightarrow \left( \dfrac{7}{3} \right)\left( \dfrac{3}{7}x \right)=4\left( \dfrac{7}{3} \right)\]
Multiplying 7 and 4 we get 28,
\[\Rightarrow x=\dfrac{28}{3}\]
Hence, the solution of the given equation is \[x=\dfrac{28}{3}\].

Note: We can check if the answer is correct or not by substituting the value in the given equation. From the given equation, we get the left-hand side as \[\dfrac{3}{7}x+5\], and right-hand side as 9. Substituting \[x=\dfrac{28}{3}\] in both sides of equation, we get LHS as \[\dfrac{3}{7}\left( \dfrac{28}{3} \right)+5\] by cancelling out the common factor from numerator and denominator we get \[4+5=9\], and RHS as 9. As \[LHS=RHS\], the solution is correct.