Download Handout on First Degree Equations

PROCEDURE FOR SOLVING FIRST DEGREE EQUATIONS
1.
If an equation has fractions (or decimals), multiply through by the least common denominator of all the
denominators in the equation. Be sure to group any numerators containing more than one term.
2.
Remove any parenthesis by employing the distributive law. (this step and step 1 can be performed in reverse
order).
3.
On each side of the equation, combine all similar terms by addition/subtraction.
4.
Add/subtract the appropriate terms so that all the terms containing the unknown are on one side, all terms
not containing the unknowns are on the other.
5.
(For literal equations only, see below for example) If the unknown is present in more than one term, factor the
unknown out of each term containing the unknown.
6.
Divide both sides of the equation by the coefficient of the unknown, or factor(s) multiplied by the unknown.
Some common errors.
1.
Don't distribute multiplication over multiplication, that is, if you need to multiply (2/5)(x - 3) by 5, multiply
only the 2/5 by 5. (that is, do not multiply the (x - 3) by 5). Thus 5(2/5)(x - 3) = 2(x - 3) =
2x - 6..
2.
Always combine terms (step 3) before performing the addition/subtraction (step 4). Given the equation:
2x + 5 - 3x - 11 = 2x + 4 - 5x - 7, add similar terms on each side of the equation before trying to
isolate the unknown. The next step should read:
-x - 6 = -3x - 3.
Now, you can proceed to isolate the x, by adding 3x + 6 to both sides.
3.
For decimal equations, multiply through by the least power of 10 (10, 100, 1000, 10000,...), which will make
all coefficients whole numbers. Clear .234x - .5 = 2x - 1.01 by multiplying through by 1000 to yield
234x - 500 = 2000x - 1010.
4.
Always divide last. So for 3x = 34 + x do not divide by 3. You must subtract x from both sides first to obtain
2x = 34. NOW you can divide by 2.
5.
(For literal equations, step 5 above) If more than one term contains the unknown, factor out the unknown first,
then divide both sides by the "other" factor(s). So in the equation where x is the unknown to be solved:
gsx - dx - x = 3sw + 7k factor out the x on the left side to obtain
x(gs - d - 1) = 3sw + 7k and then divide both sides by (gs - d - 1) to yield the solution:
x = 3sw + 7k
gs - d - 1
1
Example 1 Solve for x:
x+3
3
- 2x - 1 = - x
2
6
Example 2 Solve for w:
w+h - p+1
g
k
= 2w
2