Solving Two Step Equations
Since algebra is "undoing an equation" or "working backwards", you also work backwards from the order of operations by adding or subtracting first instead of multiplying or dividing. The other way you can think of it is to say you work with the lonely number, (the constant), the one without the variable, first.
2k + 4 = 16
- 4 - 4
2k = 12
k = 6
Inequalities are solved similar to the one step algebra problems by doing an inverse operation to both sides. The only thing that is different is an inequality sign instead of an equal sign.
******You only have to worry about flipping around the inequality sign when you multiply or divide both sides by a negative number. *** See examples below.
Ex. 2k > -16 Ex. -4y > 24
2k > -16 -4y > 24 (Notice, the inequality sign
2 2 -4 -4 switched around because I divided
k > -8 y < -6 by a negative number to both
sides of problem)
Solving Algebraic Equations with Addition & Subtraction
Show work (doing an inverse operation to both sides of the equation and your solution).
Sometimes a problem is written backwards. Always look for the variable---then do the inverse operation with the number that is with it.
EX. y + 4 = 2 (either subtract 4 EX. -15 = z - 7
-4 -4 or add negative 4) +7 +7
y = -2 -8 = z
Solving Algebraic Equations with Multiplying & Dividing
Show work (doing an inverse operation to both sides of the equation and your solution)
EX. -5x = 35 k = 4
-5x = 35 -6
-5 -5 (-6) k = 4 (-6)
x = -7 -6
k = -24
Solving Algebraic Equations with Fractions
(Use the Multiplicative Inverse Property to isolate the variable) 2/5 * 5/2 = 1
EX. 2 y = 15
( 5 ) 2 y = 15 ( 5 ) (Multiply Note: Be sure you are multiplying
2 5 1 2 fractions) by the reciprocal (the "flipped
over fraction") to both sides of
y = 75 = 37.5 the equation ---not the original
2 fraction with the variable