Term
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)
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2.)Simplify
(Square Root of (a*b)x^3))
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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.
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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.
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5.)Simplify to obtain the final result.
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Term
| What does (Square Root of "a") Multiplied by (Square Root of "b") Equal? |
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Definition
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Term
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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Term
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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Term
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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Term
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)
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2.)To make things simple, set the exponents as a subtraction problem.
(a/b)-(c/d)
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3.)Make the denominators the same
((a*d)/(b*d))-((c*b)/(d*b))
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4.)Subtract the two exponents
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5.)Apply your new exponent to the base "a"
(a^(a*d)/(b*d))-((c*b)/(d*b))
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Term
What does
(x^a)*(x^b)
Equal? |
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Definition
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Term
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
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2.)Subtract "ax" from both sides
((ax-ax)+ab=(cx-ax)+d)
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3.)Subtract "d" from both sides
((ab-d)=(cx-ax)+(d-d))
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4.)Solve for x
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Term
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))
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2.)That eliminates denominators so you end up with the following:
((e)*(ax+b))+((c)*(x+d))=(f*(c*e))
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3.)Distribute,Simplify, and Combine Like Terms
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4.)Isolate the variable on one side of the equation.
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5.)Solve for x
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Term
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)
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2.)Simplify and Solve for x
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Term
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)
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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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Term
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
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2.)Use the quadratic formula
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3.)Write your solutions in a solution set.
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Term
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)
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2.)Take the Squareroot of Both Sides
(Square Root of (x^2))
=
(Plus or Minus the Square Root of (b-a))
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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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Term
How do you solve a problem of this form?
(x^2)-ax-b=0 |
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Definition
1.)Use the Quadratic Formula
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2.)Write your solutions in a solution set.
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Term
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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Term
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
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2.)Expand and FOIL
ax+b=(x+c)*(x+c)
Which Should Become...
ax+b=(x^2)+(cx+cx)+(c^2)
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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)
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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)
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5.)Use the Quadratic Formula
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6.)Check your solutions by plugging them back into the original equation and determining whether or not they generate true statements.
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7.)Write your solution(s) in a solution set.
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Term
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
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2.)Now Use the Quadratic Formula
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3.)Check your solutions by plugging them back into the original equation and determining whether or not they generate true statements.
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4.)Write your solution(s) in a solution set.
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Term
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
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2.)Use the Quadratic Formula
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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.
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4.)Write your solutions in a solution set.
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Term
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
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2.)Use the Quadratic Formula
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3.)Substitute "e" for (ax-b) and solve for "x".
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4.)Place your solutions in a solution set.
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Term
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
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2.)Combine Like Terms
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3.)Simplify and Solve for "x".
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Term
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
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2.)Combine Like Terms
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3.)Simplify and Solve for "x".
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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" |
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Definition
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Term
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
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2.)Subtract "a" from both sides
(a-a)+(bx-cx)>(cx-cx)+(d-a)
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3.)Write Your Solution In Interval Notation and Graph it On The Number Line.
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Term
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"
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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.
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3.)Now you have a basic Inequality equation, solve for "x" and write your solution in interval notation.
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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 |
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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
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2.)Divide each part by "b"
(-a-c)/b
Less than or Equal to
bx/b
Less than or Equal to
(d-c)/b
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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
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2.)Solve both problems for "x"
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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
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2.)Solve both problems for "x"
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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
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2.)Solve both problems for "x"
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3.)Write your solutions in interval notation.
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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 to
0 |
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Definition
The solution is
{0} Union [a,infinity)
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