7. Simplify the radical: . Assume that all variablesrepresent positive numbers.

(√[45xy^17)/(√[5xy])

8. Simplify the radical expression . Assume that all variables represent positive numbers.

√[275y^15b^11]

9. Simplify and combine like radicals

√[18] - √[50] + √[98]

10. Use the quadratic formula to solve the following equation.

5 x + 6 = 14 x 2

11. Factor the trinomial. Factor out all common monomials first.

21x^3 - 52x^2 + 32x

12. Solve the equation.

x/8 = 13

13. Solve the equation.

b/3 - b/4 = 5

14. What is the slope of the line passing through the points ( 7, 2 ) and ( 0, 0 )?

15. Solve the inequality.

-4/17 < - 8/17x

16. Find the product.

- 2x (3x^2 - 5x + 8)

Solution Summary

Factoring and Solving Equations and Inequalities are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

The techniques for solving linear equationsand linear inequalities are similar, yet different. Explain and give an example of both a linear equation and a linear inequality that demonstrates this difference.
1.) Solve and check the linear equation.
5x - 5 = 30
A) {30}
B) {34}
C) {11}
D) {7}
2.) Solve and check th

In using the factoring method of solving quadratic equations, we put it in the form:
(x+a)(x+b) = 0, where a and b are two constants (think of them as two `numbers').
If the right-hand side of this equation is not zero (let us say, another constant "c"), do you think it can be solved? If so, how? If not, why not?

Explain the four steps for solving quadratic equations? Can any of the steps be eliminated? Can any of the steps be changed? Would you add any steps to make it easier, or to make it easier to understand?

1) For the equations, you are learning several methods of finding the solution to a system. Is there a difference in the result you get using an algebraic method and what you get using a graphical method? Why or why not? How does the graph of two linear equations relate to the number of solutions to the system? How could you

Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, andfactoring. What are the pros and cons of each of these methods? When might each method be most appropriate? Which method do you prefer?
Why?

Why should we clear fractions when solving linear equationsandinequalities? Demonstrate how this is done with an example.
Why should we clear decimals when solving linear equationsandinequalities? Demonstrate how this is done with an example.
Post one other example (either fraction or decimal) for classmates to solve

Topic 1: Properties of Inequalities
We have two variables A and X.
The value of X is less than the value of A
Discuss without using any specific numbers, how we can prove that the value of ( -X) is greater than the value of( -A).
Do not use any numerical examples.
Keep in mind that A or X could be any numerical va

Solving Quadratic Equations by Factoring is Chapter 13.7 page 955
1) Quadratic Equation is in STANDARD FORM (ax^2 + bx + c = 0 where a is positive)
Factor trinomial: x^2 + bx +c =(X + m)( X +n)=0 ,which :(mn=C),and (m+n=b)
(X + m)=0 ---->X = - m , and (X + n)=0----> X= - n
2) Pythagorean Theorem in Right triangle (