Procedures That Result in Equivalent Equations

1. Interchange the two sides of the equation:

Replace 3 = x by x = 3

2. Simplify the sides of the equation by combining like terms, eliminating

parentheses, and so on:

Replace 1x + 22 + 6 = 2x + 1x + 12

by x + 8 = 3x + 1

3. Add or subtract the same expression on both sides of the equation:

Replace 3x - 5 = 4

by 13x - 52 + 5 = 4 + 5

4. Multiply or divide both sides of the equation by the same nonzero

expression:

Replace 3x - 5 = 4

by 13x - 52 + 5 = 4 + 5

4. Multiply or divide both sides of the equation by the same nonzero

expression:

Replace

3x

______

x - 1 =

by 3x/x-1

5. If one side of the equation is 0 and the other side can be factored, then we

may use the Zero-Product Property* and set each factor equal to 0:

Replace x(x - 3)2 = 0

by x = 0 or x - 3 = 0

(sidebar)

Warning Squaring both sides of an

equation does not necessarily lead to

an equivalent equation. For example,

x = 3 has one solution, but x2 = 9

has two solutions, x = -3 and x = 3.

■

Example 1 solving an equation

solve the equation 3x-5 = 4

Solution Replace the original equation by a succession of equivalent equations.

3x - 5 = 4

(3x - 5) + 5 = 4 + 5 Add 5 to both sides.

3x = 9 *Simplify.*

3x/9 = 9/3 *Divide both sides by 3.*

x = 3 *Simplify*

Hi this is Kim, could you please show me an example of format in ueb/nemeth the italized words are in blue, I think I should put these in bracket with a transcriber note on transcriber's note page.

is there any way you can send in braille v2.

Thanks so much.