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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 = 4by 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.
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Example 1 solving an equationsolve 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 SimplifyHi 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.Good day, Kim.
If I understand your question correctly, you are wondering how to transcribe the series of steps with comments at the end of your sample text.
It is almost certainly not necessary to indicate that the comment text is blue. Context should make it abundantly clear to the reader what is part of the math expression and what is comment. Add to that the use of Nemeth Code switch indicators as illustrated in the attached files, and your braille reader should be very well off.
An image of the appropriate braille is attached as well as a BRF. [I am afraid it is not possible to attach a Braille2000 file at this time.]
Thank you for your question.
–Kyle
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