Question

How do you solve $-\left( x-10 \right)=7$? \[\]

Answer 1

Hint: We recall the linear equations and basic properties of linear equations. We solve the given linear equation by opening the parenthesis in the left hand and then eliminating the constant terms at the left hand side till the variable term is at one side and constant at the other side. We finally divide both sides by a coefficient of $x$ to get only $x$ at the left hand side.

Complete step by step answer:
We know from algebra that the linear equation in one variable $x$ and constants $a\ne 0,b$ is given by
\[ax=b\]
The term with which the variable is multiplied is called variable term and with whom not multiplied is called constant term. We also know that if we add, subtract, multiply or divide the same number on both sides of the equation, equality holds. It is called balancing the equation. It means for some term $c$ we have,
\[\begin{align}
  & ax+c=b+c \\
 & ax-c=b-c \\
 & ax\times c=b\times c \\
 & \dfrac{ax}{c}=\dfrac{b}{c} \\
\end{align}\]
When we are asked to solve for $x$ in an equation it means we have to find the value or values of $x$ for which the equation satisfies. We are given the following linear equation
\[\begin{align}
  & -\left( x-10 \right)=7 \\
 & \Rightarrow -1\times \left( x-10 \right)=7 \\
\end{align}\]
 We see that we are given an equation with one variable and a variable term is at only the left hand side. We first open the bracket following BODMAS rule using distributive property ot have
\[\begin{align}
  & \Rightarrow -1\times x-1\times \left( -10 \right)=7 \\
 & \Rightarrow -x+10=7 \\
\end{align}\]
We subtract both sides 10 to have;
\[\begin{align}
  & \Rightarrow -x+10-10=7-10 \\
 & \Rightarrow -x=-3 \\
\end{align}\]
We divided both sides by $-1$ which is the coefficient to have
\[\begin{align}
  & \Rightarrow \dfrac{-x}{-1}=\dfrac{-3}{-1} \\
 & \Rightarrow x=3 \\
\end{align}\]
So the solution is $x=3$.

Note:
We can alternatively solve by first multiplying $-1$ both sides of the given equation $-\left( x-10 \right)=7$to have $x-10=-1\times 7=-7$. We then add both sides by 10 to have $x-10+10=-7+10\Rightarrow x=3$. We should always try to keep variable terms at one side and constant terms at the other side. We note that the coefficient of a variable term is the constant that is multiple to the variable.