Algebra: Chapter 3, Lesson 8, page 145.
Solving Equations Involving Absolute Value
The absolute value of a number, `|x|` is its distance from zero on the number line. Remember that the absolute value is always positive. Treat absolute value equations just like those without absolute value and then solve them as normal. At the VERY END, put the absolute value symbols back in and see if the answer has ANOTHER solution.
Remember too, that we cannot have an absolute value be NEGATIVE. In these cases, there is NO SOLUTION. For example:
`|x| + 2 = 12`
`|x| + 2 + (-2) = 12 + (-2)`, we subtract 2 from both sides to isolate the variable, x
`|x| = 10`, we simplify the right side and finally,
`x=10` or `x=-10` are the solutions
This is a good purplemath.com link with examples.
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 2, Lessons 5 and Lesson 6, pages 77 and 81.
Multiplication and Division of Rational Numbers
Today is easy because the rules for multiplication and division are simple.
- When multiplying 2 numbers AND if the SIGNS are the same, the product is ALWAYS positive.
- If the signs are different, them the product is ALWAYS negative. This is pretty straightforward.
Division follows the same rules as multiplication.
2 rational numbers whose product is 1 are called multiplicative inverses or reciprocals of each other. Just flip the rational expression over and keep the same sign. For example, the reciprocal of `2/3` or `m/n` is `3/2 ` and `n/m` respectively.
Remember too, to divide rational numbers, sometimes its easier to express them as improper fractions, then convert the 2nd term to its reciprocal and change the `/` to a `⋅`.
Two of tonight’s homework problems solved by MrE are here! Just click it!
Purplemath.com has these tutorials about multiplying and dividing rational numbers, check it out!