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## Details

2-Precalculus:Homework:Notes:Test 1 Review
2-Precalculus:Homework:Notes:Test 1 Review
30
Mathematics
01/28/2016

Term
 How do you solve a problem in this form?(Square Root of ax^2)*(Square Root of bx)
Definition
 1.)Set the problem as(Square Root of (ax^2)*bx)---2.)Simplify(Square Root of (a*b)x^3))---3.)Find a Perfect Square That When Multiplied by a number equals (a*b) if possible. If this is not possible, then this is your solution.---4.)Separate your answer into two square roots. The perfect square will have the x^2 and the other number will simply have the x.---5.)Simplify to obtain the final result.---
Term
 What does (Square Root of "a") Multiplied by (Square Root of "b") Equal?
Definition
 (The Square Root of a*b)
Term
 How do you solve a problem in this form?(Square Root of (a*11)x^2)Multiplied by the(Square Root of ax)
Definition
 1.)The solution is ax(Square Root of 11x)---
Term
 How do you solve a problem in this form?(Square Root of (a*2)x^2)Multiplied by the(Square Root of ax)
Definition
 1.)The solution is ax(Square Root of 2x)---
Term
 How do you solve a problem in this form?(Square Root of (a*b)x^2)Multiplied by the(Square Root of ax)
Definition
 1.)The solution is ax(Square Root of bx)---
Term
 How do you express an answer with positive exponents if the problem is in the form of?(a^(a/b)*(a^(-c/d)
Definition
 1.)Set the exponents up as an addition problem:(a/b)+(-c/d)---2.)To make things simple, set the exponents as a subtraction problem.(a/b)-(c/d)---3.)Make the denominators the same ((a*d)/(b*d))-((c*b)/(d*b))---4.)Subtract the two exponents---5.)Apply your new exponent to the base "a"(a^(a*d)/(b*d))-((c*b)/(d*b))---
Term
 What does(x^a)*(x^b)Equal?
Definition
 (x^(a+b))
Term
 How do you solve a problem in this form?a(x+b)=cx+d
Definition
 1.)Distribute ax+ab=cx+d---2.)Subtract "ax" from both sides((ax-ax)+ab=(cx-ax)+d)---3.)Subtract "d" from both sides((ab-d)=(cx-ax)+(d-d))---4.)Solve for x---
Term
 How do you solve a problem in this form?((ax+b)/c)+((x+d)/e)=f
Definition
 1.)Multiply everything by (c*e)((c*e)*((ax+b)/c))+((c*e)*((x+d)/e))=(f*(c*e))---2.)That eliminates denominators so you end up with the following:((e)*(ax+b))+((c)*(x+d))=(f*(c*e))---3.)Distribute,Simplify, and Combine Like Terms---4.)Isolate the variable on one side of the equation.---5.)Solve for x---
Term
 What is a shortcut to solving a problem in this form? a(x+b)=cx+d
Definition
 1.)It always equals(ab-d)=(cx-ax)---2.)Simplify and Solve for x---
Term
 What is a solution to a problem of this form asking to solve for "d"?a=((b+c)d)/e
Definition
 1.)Multiply both sides by "e"(a*e)=(((b+c)d)/e)*(e)Which Becomes....ae=((b+c)d)---2.)Divide both sides by (b+c)(ae)/(b+c)=((b+c)d)/(b+c)Which Should Become...(ae)/(b+c)=d---
Term
 How do you solve a problem in this form?(x^2)=(ax)+(b)
Definition
 1.)Subtract ((ax)+(b)) from both sides(x^2)-((ax)+(b))=((ax)+(b))-((ax)+(b))Which Should Become...(x^2)-((ax)-(b))=0---2.)Use the quadratic formula---3.)Write your solutions in a solution set.---
Term
 How do you solve a problem of this form?(x^2)+a=b
Definition
 1.)Subtract "a"from both sides(x^2)+(a-a)=(b-a)Which Should Become....(x^2)=(b-a)----2.)Take the Squareroot of Both Sides(Square Root of (x^2))=(Plus or Minus the Square Root of (b-a))---3.)Type your solutions in a solution set.{(Plus the Square Root of (b-a)),(Minus the Square Root of (b-a))}---
Term
 How do you solve a problem of this form?(x^2)-ax-b=0
Definition
Term
 How do you solve a problem in this form?(a-i)+(-b+ci)
Definition
 1.)Combine Like Terms(a-b)+(ci-i)----
Term
 How do you solve a problem of this form?(x/(x-a)-(a/(x+a))=((2a)*x)/(x^2)-(a^2))
Definition
 1.) There is no solution---
Term
 How do you solve a problem of this form?(Square Root of ax+b)=(x+c)
Definition
 1.)Square both sides(Square Root of ax+b)^2=(x+c)^2Which Should Become...ax+b=(x+c)^2---2.)Expand and FOILax+b=(x+c)*(x+c)Which Should Become...ax+b=(x^2)+(cx+cx)+(c^2)---3.)Subtract "b" from both sidesax+(b-b)=(x^2)+(cx+cx)+(c^2-b)Which Should Become...ax=(x^2)+(cx+cx)+(c^2-b)---4.)Subtract "ax" from both sides(ax-ax)=(x^2)+((cx+cx)-ax)+(c^2-b)Which Should Become...0=(x^2)+((cx+cx)-ax)+(c^2-b)---5.)Use the Quadratic Formula---6.)Check your solutions by plugging them back into the original equation and determining whether or not they generate true statements.----7.)Write your solution(s) in a solution set.---
Term
 What is a Shortcut to Solving a problem of this form?(Square Root of ax+b)=(x+c)
Definition
 1.)The Problem Becomes This, So just Skip to this Step.(x^2)+((cx+cx)-ax)+(c^2-b)=0---2.)Now Use the Quadratic Formula---3.)Check your solutions by plugging them back into the original equation and determining whether or not they generate true statements.----4.)Write your solution(s) in a solution set.---
Term
 How do you solve a problem in this form?(x^4)-(ax^2)+b=0
Definition
 1.)Let "c" equal (x^2) and Substitute(c^2)-(ac)+b=0---2.)Use the Quadratic Formula---3.)Now you should have two solutions for "c". Replace "c" with (x^2) and solve for "x". Each Solution for "x" is plus or minus that solution. ----4.)Write your solutions in a solution set.---
Term
 How do you solve a problem of this form?((ax-b)^2)+c(ax-b)-d=0
Definition
 1.)Let "e" equal (ax-b) and Substitute(e^2)+(ce)-d=0---2.)Use the Quadratic Formula---3.)Substitute "e" for (ax-b) and solve for "x".---4.)Place your solutions in a solution set.---
Term
 How do you solve a problem in this form?(-ax)-b(c-bx)=b(x-d)-e
Definition
 1.)Distribute(-ax)(-bc+(b*bx)=(bx-bd)-e---2.)Combine Like Terms---3.)Simplify and Solve for "x".---
Term
 How do you solve a problem in this form?(-ax)-b(c-dx)=e(x-f)-g
Definition
 1.)Distribute(-ax)(-bc+b(dx))=(ex-ef)-g----2.)Combine Like Terms---3.)Simplify and Solve for "x".---
Term
 How do you write the inequality notation and graph the interval of an inequality in this form?"-a" is less than "x" is less than or Equal to " b"
Definition
 1.) (-a,b]----
Term
 How do you solve a problem in this form?a+bx>cx+d
Definition
 1.)Subtract "cx" from both sidesa+(bx-cx)>(cx-cx)+d----2.)Subtract "a" from both sides(a-a)+(bx-cx)>(cx-cx)+(d-a)---3.)Write Your Solution In Interval Notation and Graph it On The Number Line.---
Term
 How do you solve a problem of this form?(x-a)/bGreater Than or Equal To(x/c)+d
Definition
 1.)Multiply both sides by "bc" ---2.)This should remove the denominators from both sides and "d" should have also been multiplied by "bc".Now Distribute "c" on the left side, and "b" on the right side. ---3.)Now you have a basic Inequality equation, solve for "x" and write your solution in interval notation.---
Term
 How do you solve a combined inequality in this form?-aLess than or Equal tobx+cLess than or Equal tod
Definition
 1.)Subtract "c" from each part-a-cLess than or Equal tobx+(c-c)Less than or Equal tod-c---2.)Divide each part by "b"(-a-c)/bLess than or Equal tobx/bLess than or Equal to(d-c)/b---3.)Write your solutions in Interval Notation.---
Term
 How do you solve a problem in this form?|ax-b|=c
Definition
 1.)Set the problem as two problems:ax-b=c ax-b=-c---2.)Solve both problems for "x"---3.)Write your solutions in a solution set.---
Term
 How do you solve a problem in this form?|x+a| is less than b
Definition
 1.)Set as two problemsx+a is less than b x+a is greater than -b---2.)Solve both problems for "x"---3.)Write your solutions in interval notation.---
Term
 How do you solve a problem in this form?|a-bx|>c
Definition
 1.)Set the problem as two problemsa-bx>ca-bx<-c---2.)Solve both problems for "x"---3.)Write your solutions in interval notation.---
Term
 How do you use the test-point method to solve a polynomial inequality in this form?(x^3)-(ax^2)Greater than or equal to0
Definition
 The solution is{0} Union [a,infinity)---
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