Usually, equations won’t come with varying terms and constant terms lined up on separate sides. In the example above, the left-hand side (LHS) has both varying and constant terms, as does the right-hand side (RHS).
The equation 16x−5x=32−10{\displaystyle 16x-5x=32-10} does have all the varying terms on one side (LHS), while all the constant terms are on the other side (RHS).
In example 1, 7x−10=3x−6{\displaystyle 7x-10=3x-6} can be rearranged by choosing to subtract either 7x{\displaystyle 7x} or 3x{\displaystyle 3x} from both sides. Choosing to subtract 7x{\displaystyle 7x}, you have:(7x−7x)−10=(3x−7x)−6−10=−4x−6{\displaystyle {\begin{aligned}(7x-7x)-10&=(3x-7x)-6\-10&=-4x-6\end{aligned}}}
We see that −6{\displaystyle -6} must be subtracted from both sides:−10−(−6)=−4x−6−(−6)−4=−4x{\displaystyle {\begin{aligned}-10-(-6)&=-4x-6-(-6)\-4&=-4x\end{aligned}}}
The coefficient of x{\displaystyle x} in −4x{\displaystyle -4x} is −4{\displaystyle -4}. So divide both sides by −4{\displaystyle -4} to get the value of x=1{\displaystyle x=1}. Our answer to the equation 7x−10=3x−6{\displaystyle 7x-10=3x-6} is x=1{\displaystyle x=1}. You can check this answer by plugging 1{\displaystyle 1} back into every x{\displaystyle x} variable and seeing if both sides of the equation equal the same number:7(1)−10=3(1)−6−3=−3{\displaystyle {\begin{aligned}7(1)-10&=3(1)-6\-3&=-3\end{aligned}}}
In this example, the coefficient of x{\displaystyle x} in 11x{\displaystyle 11x} is 11{\displaystyle 11}. That division is 11x/11=22/11{\displaystyle 11x/11=22/11} to get x=2{\displaystyle x=2}. The answer to the equation 16x−5x=32−10{\displaystyle 16x-5x=32-10} is x=2{\displaystyle x=2}.
