# Solve the Inequality for x 2x^2-7x+3>0

Convert the inequality to an equation.

Factor by grouping.

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For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

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Factor out of .

Rewrite as plus

Apply the distributive property.

Factor out the greatest common factor from each group.

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Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set equal to and solve for .

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Set equal to .

Solve for .

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Add to both sides of the equation.

Divide each term in by and simplify.

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Divide each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Set equal to and solve for .

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Set equal to .

Add to both sides of the equation.

The final solution is all the values that make true.

Use each root to create test intervals.

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

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Test a value on the interval to see if it makes the inequality true.

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Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

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Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is not greater than the right side , which means that the given statement is false.

False

False

Test a value on the interval to see if it makes the inequality true.

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Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Compare the intervals to determine which ones satisfy the original inequality.

True

False

True

True

False

True

The solution consists of all of the true intervals.

or

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

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