How to Solve a Simple Linear Equation

Step-by-Step Guide

1. 1

   Step 1: Look at your problem.

   A simple linear equation might look like 7x−10=3x−6{\displaystyle 7x-10=3x-6}. , Varying terms are numbers like 7x{\displaystyle 7x}, 3x{\displaystyle 3x}, 6y{\displaystyle 6y} or 10z{\displaystyle 10z}, where the number changes depending on what you plug into the variable, or letter.
   
   Constant terms are numbers like 10{\displaystyle 10}, 6{\displaystyle 6} or 30{\displaystyle 30}, where the number never changes.
   
   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). , In order to do this, you may have to subtract or add the numbers you want to move from both sides.
   
   In the next step, you'll see how to do that in example
   1.
   
   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). , It doesn't matter to which side you move the varying terms.
   
   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}}} , That is: move the constant terms so that they are on the opposite side of the equation from where the varying terms are.
   
   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} (or y{\displaystyle y}, or z{\displaystyle z}, or any letter) is the number in front of the varying term.
   
   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}}}
2. 2

   Step 2: Check the equation for varying terms and constant terms.

3. 3

   Step 3: Prepare to move the numbers around so that the varying terms are on one side and the constant terms are on the side such as in 16x−5x=32−10{\displaystyle 16x-5x=32-10} (that equation is solved in example 2).

4. 4

   Step 4: Move the varying terms to one side of the equation.

5. 5

   Step 5: Bring all the constant terms onto the other side of the equation.

6. 6

   Step 6: Divide both sides by the coefficient of x{\displaystyle x}.

Detailed Guide

About the Author