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.
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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
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is there any way you can send in braille v2.
Thanks so much.