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


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


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 ((axax)+ab=(cxax)+d)  3.)Subtract "d" from both sides ((abd)=(cxax)+(dd))  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 (abd)=(cxax)  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)+(aa)=(ba) Which Should Become.... (x^2)=(ba)  2.)Take the Squareroot of Both Sides (Square Root of (x^2)) = (Plus or Minus the Square Root of (ba))  3.)Type your solutions in a solution set. {(Plus the Square Root of (ba)),(Minus the Square Root of (ba))}  


Term
How do you solve a problem of this form? (x^2)axb=0 

Definition
1.)Use the Quadratic Formula  2.)Write your solutions in a solution set.  


Term
How do you solve a problem in this form? (ai)+(b+ci) 

Definition
1.)Combine Like Terms (ab)+(cii)  


Term
How do you solve a problem of this form? (x/(xa)(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)^2 Which Should Become... ax+b=(x+c)^2  2.)Expand and FOIL ax+b=(x+c)*(x+c) Which Should Become... ax+b=(x^2)+(cx+cx)+(c^2)  3.)Subtract "b" from both sides ax+(bb)=(x^2)+(cx+cx)+(c^2b) Which Should Become... ax=(x^2)+(cx+cx)+(c^2b)  4.)Subtract "ax" from both sides (axax)=(x^2)+((cx+cx)ax)+(c^2b) Which Should Become... 0=(x^2)+((cx+cx)ax)+(c^2b)  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^2b)=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? ((axb)^2)+c(axb)d=0 

Definition
1.)Let "e" equal (axb) and Substitute (e^2)+(ce)d=0  2.)Use the Quadratic Formula  3.)Substitute "e" for (axb) and solve for "x".  4.)Place your solutions in a solution set.  


Term
How do you solve a problem in this form? (ax)b(cbx)=b(xd)e 

Definition
1.)Distribute (ax)(bc+(b*bx)=(bxbd)e  2.)Combine Like Terms  3.)Simplify and Solve for "x".  


Term
How do you solve a problem in this form? (ax)b(cdx)=e(xf)g 

Definition
1.)Distribute (ax)(bc+b(dx))=(exef)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


Term
How do you solve a problem in this form? a+bx>cx+d 

Definition
1.)Subtract "cx" from both sides a+(bxcx)>(cxcx)+d  2.)Subtract "a" from both sides (aa)+(bxcx)>(cxcx)+(da)  3.)Write Your Solution In Interval Notation and Graph it On The Number Line.  


Term
How do you solve a problem of this form? (xa)/b Greater 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? a Less than or Equal to bx+c Less than or Equal to d 

Definition
1.)Subtract "c" from each part ac Less than or Equal to bx+(cc) Less than or Equal to dc  2.)Divide each part by "b" (ac)/b Less than or Equal to bx/b Less than or Equal to (dc)/b  3.)Write your solutions in Interval Notation.  


Term
How do you solve a problem in this form? axb=c 

Definition
1.)Set the problem as two problems: axb=c axb=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 problems x+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? abx>c 

Definition
1.)Set the problem as two problems abx>c
abx<c  2.)Solve both problems for "x"  3.)Write your solutions in interval notation.  


Term
How do you use the testpoint method to solve a polynomial inequality in this form? (x^3)(ax^2) Greater than or equal to 0 

Definition
The solution is {0} Union [a,infinity)  

