Solving Linear Inequalities in One Variable
(vertically  using the balance beam )
Solve Equation with a Balance Beam
Pattern: ax + b ≥ cx + d
Both sides simplified (a ,b, c, d are integers.)
Look at the coefficients of x and determine which is the larger integer (furthest to the right on
the number line). If c > a then we will keep the variiablle x on that siide of the equation and keep
the constant on the other side. To do this we first add opposites on the balance beam below the
equation. Look at the pattern, and then follow the same steps through several examples
Solve simplified equations vertically  using the balance beam.
Pattern: c > a
1) Add opps: 

c > a → c  a > 0 
Complete the step: 
(b  d) ≥ (c  a)x →

Let A = (c  a) and B = (b  d)
A, B are integers, A > 0 
2) Multiply recip: Then: 
→
→ 
Since
and
A > 0 is coefficient of x 
Equivalent Property
This means that all replacement values for x will be on or to the left of
NOTE: Since A > 0 all signs in its path remain the same. This
is the advantage of choosing the side of larger coefficient when simplifying the problem.
