Question

How do you solve \[3-7x=10\]?

Answer 1

Hint: The given equation is a linear equation in one variable. We know that to solve these types of equation or to find the solution value of the variable, we need to take the variable terms to one side of the equation and constants to the other side of the equation. The given equation has only one variable term in it \[-3x\] on its left side along with a constant value 3. So, to solve this equation we need to take this constant term to the right side which has 10.

Complete step by step solution:
We are given the equation \[3-7x=10\], 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.
\[3-7x=10\]
Subtracting 3 from both sides of the above expression, we get
\[\Rightarrow -7x=10-3=7\]
Multiplying \[-1\] to both sides of above equation, we get
\[\begin{align}
  & \Rightarrow -1\left( -7x \right)=-1\left( 7 \right) \\
 & \Rightarrow 7x=-7 \\
\end{align}\]
Dividing both sides of the above equation by 7, we get
\[\Rightarrow x=-1\]
Hence, the solution of the given equation is \[x=-1\].

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 \[3-7x\], and the right-hand side as 10. Substituting \[x=-1\] in both sides of the equation, we get LHS as \[3-7(-1)=3+7=10\], and RHS as 10. As \[LHS=RHS\], the solution is correct.