Question

How do you solve \[\dfrac{x}{3} + 10 = 15\]?

Answer 1

Hint: Here, we need to solve the linear equation. A linear equation is defined as an equation which has the highest degree of the variable as 1 and it can be solved using basic mathematical operations. We will use the basic mathematical operations like addition, subtraction, multiplication, and division to find the value of \[x\].

Complete step-by-step answer:
We will use the operations of addition, subtraction, multiplication, and division to find the value of \[x\].
First, we will isolate the term with the variable on one side of the equation.
Subtracting 10 from both sides of the equation \[\dfrac{x}{3} + 10 = 15\], we get
\[ \Rightarrow \dfrac{x}{3} + 10 - 10 = 15 - 10\]
Thus, we get
\[ \Rightarrow \dfrac{x}{3} = 5\]
Thus, we have isolated the term with the variable on the left hand side of the equation.
Multiplying both sides of the equation by 3, we get
\[ \Rightarrow 3 \cdot \dfrac{x}{3} = 3 \cdot 5\]
Therefore, we get
\[ \Rightarrow x = 15\]
Thus, we get the required value of \[x\] as 15.

Note: A linear equation in one variable can be written in the form \[ax + b = 0\], where \[a\] is not equal to 0, and \[a\] and \[b\] are real numbers. For example, \[x - 100 = 0\] and \[100P - 566 = 0\] are linear equations in one variable \[x\] and \[P\] respectively. A linear equation in one variable has only one solution.
Verification: We can check our answer by substituting the obtained value of \[x\] in the given equation to check our results.
If the left hand side is equal to the right hand side, then our answer is correct.
Substituting \[x = 15\] in the left hand side (L.H.S.) of the given equation \[\dfrac{x}{3} + 10 = 15\], we get
\[ \Rightarrow {\rm{L}}{\rm{.H}}{\rm{.S}}{\rm{.}} = \dfrac{{15}}{3} + 10\]
Dividing 15 by 3 in the expression, we get
\[ \Rightarrow {\rm{L}}{\rm{.H}}{\rm{.S}}{\rm{.}} = 5 + 10\]
Adding 5 and 10 in the expression, we get
\[ \Rightarrow {\rm{L}}{\rm{.H}}{\rm{.S}}{\rm{.}} = 15\]
The right hand side of the equation can be written as
\[ \Rightarrow {\rm{R}}{\rm{.H}}{\rm{.S}}{\rm{.}} = 15\]
Therefore, we can observe that
\[ \Rightarrow {\rm{L}}{\rm{.H}}{\rm{.S}}{\rm{.}} = {\rm{R}}{\rm{.H}}{\rm{.S}}{\rm{.}}\]
Thus, the value \[x = 15\] satisfies the given equation.
Hence, we have verified our answer.