# Math inequality problem

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Can anyone please help me solve this problem:

Find the values of x for which x^2(x−4)>(x−12)

Find the values of x for which x^2(x−4)>(x−12)

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#2

Put everything onto one side so you have a cubic on one side and 0 on the other. Then try if you can factorise the cubic and draw a graph of it. Shade in the areas that satisfy the inequality.

Last edited by GrayestOwl0900; 1 year ago

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#3

X²(x-4)>(x-12)

If we are to find x, expand the left hand equation then collect like terms

This will be:

X³-4x²>X-12

Rewriting gives

X³-4x²-X+12>0

This is a cubic function. So we solve it this way

X² -X-4

X³-4x²-X+12

X-3. X³-3x²

-X²-X+12

-X²+3X

-4X+12

-4X+12

=0

So we solve

X³-4x²-X+12 using long division method, first we find the factors of the equation by substituting values, the one that gives you zero is a factor of X³-4x²-X+12

And I found that X=3 is a factor so X-3=0 is a factor of the equation.

We use long division to factorize the equation as show above.

So the equation can be written as X-3(X²-X-4)=0

So here we can introduce our inequality.

X-3(X²-X-4)>0

We solve the quadratic equation in bracket first using the quadratic formula you will have two values of x

So the final answer will have 3 values of x. Since it is a cubic function.

X>3, and the other 2 values of x you will get after solving the quadratic equation X²-X-4 let's say first value will be a, and second value be b. The answer will be

X>3

X>a

X>b

Thanks for reading

Collecting like terms

If we are to find x, expand the left hand equation then collect like terms

This will be:

X³-4x²>X-12

Rewriting gives

X³-4x²-X+12>0

This is a cubic function. So we solve it this way

X² -X-4

X³-4x²-X+12

X-3. X³-3x²

-X²-X+12

-X²+3X

-4X+12

-4X+12

=0

So we solve

X³-4x²-X+12 using long division method, first we find the factors of the equation by substituting values, the one that gives you zero is a factor of X³-4x²-X+12

And I found that X=3 is a factor so X-3=0 is a factor of the equation.

We use long division to factorize the equation as show above.

So the equation can be written as X-3(X²-X-4)=0

So here we can introduce our inequality.

X-3(X²-X-4)>0

We solve the quadratic equation in bracket first using the quadratic formula you will have two values of x

So the final answer will have 3 values of x. Since it is a cubic function.

X>3, and the other 2 values of x you will get after solving the quadratic equation X²-X-4 let's say first value will be a, and second value be b. The answer will be

X>3

X>a

X>b

Thanks for reading

Collecting like terms

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#4

(Original post by

X²(x-4)>(x-12)

If we are to find x, expand the left hand equation then collect like terms

This will be:

X³-4x²>X-12

Rewriting gives

X³-4x²-X+12>0

This is a cubic function. So we solve it this way

X² -X-4

X³-4x²-X+12

X-3. X³-3x²

-X²-X+12

-X²+3X

-4X+12

-4X+12

=0

So we solve

X³-4x²-X+12 using long division method, first we find the factors of the equation by substituting values, the one that gives you zero is a factor of X³-4x²-X+12

And I found that X=3 is a factor so X-3=0 is a factor of the equation.

We use long division to factorize the equation as show above.

So the equation can be written as X-3(X²-X-4)=0

So here we can introduce our inequality.

X-3(X²-X-4)>0

We solve the quadratic equation in bracket first using the quadratic formula you will have two values of x

So the final answer will have 3 values of x. Since it is a cubic function.

X>3, and the other 2 values of x you will get after solving the quadratic equation X²-X-4 let's say first value will be a, and second value be b. The answer will be

X>3

X>a

X>b

Thanks for reading

Collecting like terms

**BreenaBEE**)X²(x-4)>(x-12)

If we are to find x, expand the left hand equation then collect like terms

This will be:

X³-4x²>X-12

Rewriting gives

X³-4x²-X+12>0

This is a cubic function. So we solve it this way

X² -X-4

X³-4x²-X+12

X-3. X³-3x²

-X²-X+12

-X²+3X

-4X+12

-4X+12

=0

So we solve

X³-4x²-X+12 using long division method, first we find the factors of the equation by substituting values, the one that gives you zero is a factor of X³-4x²-X+12

And I found that X=3 is a factor so X-3=0 is a factor of the equation.

We use long division to factorize the equation as show above.

So the equation can be written as X-3(X²-X-4)=0

So here we can introduce our inequality.

X-3(X²-X-4)>0

We solve the quadratic equation in bracket first using the quadratic formula you will have two values of x

So the final answer will have 3 values of x. Since it is a cubic function.

X>3, and the other 2 values of x you will get after solving the quadratic equation X²-X-4 let's say first value will be a, and second value be b. The answer will be

X>3

X>a

X>b

Thanks for reading

Collecting like terms

Also, the last set of inequalities are not correct.

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#6

(Original post by

The values of a and be you find them from the quadratic equation they represent x

**BreenaBEE**)The values of a and be you find them from the quadratic equation they represent x

x>a

X>b

X>3

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#8

(Original post by

Correct where there is a mistake please. That's why we are here to learn

**BreenaBEE**)Correct where there is a mistake please. That's why we are here to learn

You have , which is a product of

**two**expressions being greater than zero.

A product is greater than zero ONLY when both expressions are *either* greater than zero, or less than zero. These are your two cases. Mathematically, this means;

Case 1:

**and**

Case 2:

**and**.

So you need to solve both cases for a range of values of satisfying them, then join them together and that's the overall range of values for which our cubic is greater than zero.

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