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Linear Equations and Literal Equations

Equality and Balances

- Will this balance? If not, which way will it tilt?

- How could we make it balance?

Exercise Draw a picture of what the following

would look like on balance scales.

- 2 ( 3 x 5 ) 7 ( 2 x 5 ) 1
- 3 ( 2 x 4 ) 1 ( 2 x 6 ) 2
- ( 10 / 2 ) ( 3 x 2 ) ( 8 / 2 ) x ( 6 / 3)

- http//illuminations.nctm.org/ActivityDetail.aspx?

id26

Find the possible missing values to balance the

equations

A linear equation in one variable is an equation

that can be written in the form

ax b 0

where a and b are

real numbers and a is not zero.

- Examples
- 4x 2 0
- 4x 4
- 2x 3x - 1

- We solve linear equations in x by transforming

the equation to an equivalent equation of the

form - x d
- where d is a real number.
- (That is we get x by itself on one side.)
- The solution set is d .
- example x 2 4 is equivalent to x 6

Properties of Equality

- Let A, B, and C be real numbers.
- If A B is a true statement, then the following

are also true - A C B C
- A C B C
- AC BC
- A/C B/C (unless C 0)

- Solving equations on a balance scale applet
- http//nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2

.html?openinstructions

Solving Equations with Two Color Chips and Cups

- Activity Packet p. 169

Solving Equations with Two-Color Counters and

Pattern Blocks

- Activity Packet p. 173

Solving Equations involving fractions with

two-color counters and pattern blocks.

- Activity packet p. 175

- A literal equation is an equation with two or

more unknowns. - A formula is an equation that models a known

relationship between two or more quantities. - Examples
- Solve A ½ bh for h.
- Solve A P Prt for P. P.

181

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