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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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## Some Examples

Example 1:

 Add opps: Complete the step: Then Check: Note: (5 â€“ 2) = 3 the coefficient of x is 1. [Replace x with 3 to check.]

Example 2:

 Add opps: Complete the step: Then Check: Note: the coefficient of x is 1. [Replace x with to check.]

## Solve Equation with Balance Beam

Pattern: a x + b = c x + d

Both sides are siimplliiffiied and 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

 1) Add opps: Complete the step: Then: Let A = (c â€“ a) and B = (b â€“ d) A = 1 is coefficient of x

Example 1:

 Add opps:Complete step: Then: Thus: Note that 3 > 2 Add same to both sides   (3 â€“ 2) = 1 and (5 + 4) = 9 Check:   or Note 3 Â· 9 = 27   x = 9 is correct

Some problems have parentheses that have to be removed and terms rearranged before working with the balance beam. Use the distributive property and associative property to simplify before solving.

Example 2:

 Add opps:Complete step: Then: Thus: 4(2x + 1) = 7(x â€“ 1) + (2 â€“ 6) 8x + 4 = (7x â€“ 7) â€“ 4 8x + 4 = 7x + (â€“ 7 â€“ 4) Distributive PropertyAssociative Property Note that 8 > 7 Add same to both sides   (8 â€“ 7) = 1 and (-11 â€“ 4) = -15

Check:

4[2(-15) + 1] = 7[(-15) â€“ 1] + (2 â€“ 6)

4[-30 + 1] = 7(-16) â€“ 4

4(-29) = -112 â€“ 4

or -116 = -116 x = -15 is correct