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How do you solve a problem in this form? (Square Root of ax^2)*(Square Root of bx) |
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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. --- |
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What does (Square Root of "a") Multiplied by (Square Root of "b") Equal? |
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Definition
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How do you solve a problem in this form? (Square Root of (a*11)x^2) Multiplied by the (Square Root of ax) |
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Definition
1.)The solution is ax(Square Root of 11x) --- |
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How do you solve a problem in this form? (Square Root of (a*2)x^2) Multiplied by the (Square Root of ax) |
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Definition
1.)The solution is ax(Square Root of 2x) --- |
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How do you solve a problem in this form? (Square Root of (a*b)x^2) Multiplied by the (Square Root of ax) |
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Definition
1.)The solution is ax(Square Root of bx) --- |
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How do you express an answer with positive exponents if the problem is in the form of? (a^(a/b)*(a^(-c/d) |
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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)) --- |
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What does (x^a)*(x^b) Equal? |
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Definition
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How do you solve a problem in this form? a(x+b)=cx+d |
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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 --- |
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How do you solve a problem in this form? ((ax+b)/c)+((x+d)/e)=f |
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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 --- |
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What is a shortcut to solving a problem in this form? a(x+b)=cx+d |
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Definition
1.)It always equals (ab-d)=(cx-ax) --- 2.)Simplify and Solve for x --- |
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What is a solution to a problem of this form asking to solve for "d"? a=((b+c)d)/e |
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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 --- |
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How do you solve a problem in this form? (x^2)=(ax)+(b) |
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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. --- |
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How do you solve a problem of this form? (x^2)+a=b |
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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))} --- |
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How do you solve a problem of this form? (x^2)-ax-b=0 |
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Definition
1.)Use the Quadratic Formula --- 2.)Write your solutions in a solution set. --- |
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How do you solve a problem in this form? (a-i)+(-b+ci) |
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Definition
1.)Combine Like Terms (a-b)+(ci-i) ---- |
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How do you solve a problem of this form? (x/(x-a)-(a/(x+a))=((2a)*x)/(x^2)-(a^2)) |
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Definition
1.) There is no solution --- |
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Term
How do you solve a problem of this form? (Square Root of ax+b)=(x+c) |
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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+(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. --- |
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What is a Shortcut to Solving a problem of this form? (Square Root of ax+b)=(x+c) |
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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. --- |
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How do you solve a problem in this form? (x^4)-(ax^2)+b=0 |
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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. --- |
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How do you solve a problem of this form? ((ax-b)^2)+c(ax-b)-d=0 |
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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. --- |
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How do you solve a problem in this form? (-ax)-b(c-bx)=b(x-d)-e |
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Definition
1.)Distribute (-ax)(-bc+(b*bx)=(bx-bd)-e --- 2.)Combine Like Terms --- 3.)Simplify and Solve for "x". --- |
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How do you solve a problem in this form? (-ax)-b(c-dx)=e(x-f)-g |
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Definition
1.)Distribute (-ax)(-bc+b(dx))=(ex-ef)-g ---- 2.)Combine Like Terms --- 3.)Simplify and Solve for "x". --- |
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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" |
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Definition
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How do you solve a problem in this form? a+bx>cx+d |
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Definition
1.)Subtract "cx" from both sides a+(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. --- |
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How do you solve a problem of this form? (x-a)/b Greater Than or Equal To (x/c)+d |
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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. --- |
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How do you solve a combined inequality in this form? -a Less than or Equal to bx+c Less than or Equal to d |
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Definition
1.)Subtract "c" from each part -a-c Less than or Equal to bx+(c-c) Less than or Equal to d-c --- 2.)Divide each part by "b" (-a-c)/b Less than or Equal to bx/b Less than or Equal to (d-c)/b --- 3.)Write your solutions in Interval Notation. --- |
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Term
How do you solve a problem in this form? |ax-b|=c |
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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. --- |
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Term
How do you solve a problem in this form? |x+a| is less than b |
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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. --- |
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Term
How do you solve a problem in this form? |a-bx|>c |
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Definition
1.)Set the problem as two problems a-bx>c
a-bx<-c --- 2.)Solve both problems for "x" --- 3.)Write your solutions in interval notation. --- |
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How do you use the test-point method to solve a polynomial inequality in this form? (x^3)-(ax^2) Greater than or equal to 0 |
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Definition
The solution is {0} Union [a,infinity) --- |
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