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/
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