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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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# Multiplication Property of Equality

## Examples

Example 1:

Solve

 Multiply recip: Distributive Property Associative Property Recall

Example 2:

 Multiply recip: Distributive Property Associative Property Note Check: Replace x with to check.

## Solve Equation with a Balance Beam

Pattern: ax + b = cx + d

Both sides siimplliiffiied (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 tthatt 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

Complete the step: (b - d) = (c - a)x Let A = (c - a) and B = (b - d)

Then: B = A x A > 1 is coefficient of x

2) Multiply recip:

→ Since

Example 3:

Solve

 1) Add opps: Note that 6 > 2(Add same to both sides) Complete the step: (6 - 2)x = (5 + 3) Now (6 - 2) = 4 and (5 + 3) = 84 is the coefficient of x 2) Multiply recip: Then x = 2 Since 3) Check: Note that 6 Â· 2 = 12  x = 2 is correct.