Sorry for the late updates

hi its karam
sorry that their wasnt anything posted, well now i will. In the couple of days we learned about Radical Equation and absolute value equations and graphing absolute values.
Here are a couple of examples from the booklets we got:

Radical Equation

(2√9k - 9)² = (18)² First you square both sides, which cancels the √

4(9k - 9) = 324 Then you multiply the 4 to the brackets

36k -36 = 324 After that move the 36 to the other side

36k = 360 Divide both sides by 36

k = 10 Final answer is 10

After that is done we need to check

2√9(10) - 9 = 18

2√90 - 9 = 18

2√81 = 18

2(9) = 18

18 = 18

so the value for k is 10

example 2 :

√b + 1 - 4 = 6 Move the 4 over

√b + 1 = 10 You square both sides, which cancels the √

b + 1 = 100 Move the 1 over

b = 99 The answer is 99

check

√99 + 1 - 4 = 6

√100 - 4 = 6

10 - 4 = 6

6 = 6

so the solution is b = 99

Now lets do Absolute Value equations

First example

⎥X + 8⎥ = 1

(x + 8) = 1

X = -7

Or

-⎥X + 8⎥ = 1

-X - 8 = 1

-X = 9

Now lets check

⎥-7 + 8⎥ = 1

⎥1⎥ = 1

⎥-9 + 8⎥ = 1

⎥-1⎥ = 1

1 = 1

X can equal -7 and -9

Now lets go to our second example

⎥6n⎥ = 24

⎥n⎥ = 4

Check

⎥6(4)⎥ = 24

⎥24⎥ = 24

Or

⎥6n⎥ = 24

⎥n⎥ = -4

Check

⎥6(-4)⎥ = 24

⎥-24⎥ = 24

⎥24⎥ = 24

n can equal -4 or 4

Graphing absolute value graph

An absolute value of a function means, only the positive value of the function will be draw since absolute values are positive.

That is if y = lxl, y is positive even for negative values of x. For example if x = -1, then y = l-1l = 1 then the -1 changes to 1. Let us see the change in the graphs when the function is defined as y = lxl

Figure 1 shows the graph of the function y = x and figure 2 shows the function y = lxl. In figure 2, the portion below the x- axis is just reflected above the x- axis.

y = lx + 3l - 1, the graph would be like this.