Algebra: Chapter 11, Lesson 9, page 519.
Equations with Radicals
A radical equation contains a variable in the radicand. To solve radical equations, first convert them to equations without radicals.
Just like taking the square root of 2 sides of an equation, you can also SQUARE both sides of an equation. This is helpful when you have radicals (square roots), because the square of a square root is just the thing in the radical!
For example:
`sqrt(2x) – 4 = 7`
first add 4 to both sides of the equation
`sqrt(2x) = 11`
now square both sides
`(sqrt(2x))^2 = 11^2`
and finally
`2x = 121` dividing by 2 yields the final answer `x = 121/2`
Don’t forget too, that sometimes you can have extraneous solutions, i.e., the answer doesn’t work so … you SHOULD check your answers by plugging them in and see if they WORK!
Click here for more information and examples!
Two of tonight’s homework problems solved by MrE are here! Just click it.
======================================================================
Algebra 1a: Chapter 9, Lesson 4, page 413.
Inequalities and Absolute Value
If the inequality with absolute values looks like: `| A | < b`, then we solve the conjunction `-b < A < b`. Think of a number line, and the solution will be within the bounds of `-b` and `b`. This also works with `≤`.
If the inequality with absolute values look like: `| A | > b`, then we solve the disjunction `A < -b` OR `A > b`. On the number line, these solutions look like arrows on the outside of the values `-b` and `b`. This works for `≥` as well.
Two of tonight’s homework problems solved by MrE are here! Just click it