Solving a Linear Equation in One Variable

Date: 02/27/98 at 00:00:17
From: gilbert
Subject: Algebra

Please help me with following algebra problems.

Solve for q:

   -13 - q - 9 = 5q - 9 - q.

Solve for w:

   4(w-5) -5 = -9 - w + 7.

Date: 02/27/98 at 09:05:05
From: Doctor Rob
Subject: Re: Algebra

Your first aim is to get all terms involving w to one side of the 
equation (say the left), and all other terms to the other side. Before 
doing that, simplify the equation by combining like terms on  each 
side.

In the first equation, after simplifying, you have:

   -q - 22 = 4*q - 9.

In general, if a term is on the "wrong" side of the equation, add its
negative to both sides of the equation.  This tells you to add 22 to 
both sides and then add -4*q to both sides.  This achieves your first 
aim.  Now simplify again by combining like terms.  You should get

   -5*q = 13.

Your final aim is to end up with an equation of the form "q = ...".  
To achieve that, you need to divide both sides by the coefficient of 
q, which is -5 in this case.  Then one last simplification (cancelling 
common factors from the numerator and denominator), and you are done.

Now use the same technique on your other problem. You will have to 
start by expanding the expression 4*(w-5).

In summary, this is the series of steps to take when solving a linear 
(degree 1) equation in one variable:

   1. Expand anything using parentheses, and combine like terms.
   2. Move all terms involving the variable to one side, all others 
      to the other side.
   3. Combine like terms.
   4. Divide by the coefficient of the variable.
   5. Reduce fractions to lowest terms.

-Doctor Rob, The Math Forum
Check out our web site http://mathforum.org/dr.math/