How do you solve #-2 + 7x - 3x^2<0#?

1 Answer
Jul 4, 2015

Answer:

(#-∞, 1/3#) and (#2, ∞#)

Explanation:

#-2 + 7x -3x^2 < 0#

One way to solve this inequality is to use a sign chart.

Step 1. Write the inequality in standard form.

#-3x^2 +7x -2 < 0#

Step 2. Multiply the inequality by #-1#.

#3x^2 -7x +2 > 0#

Step 3. Find the critical values.

Set #f(x) =3x^2 -7x +2 = 0# and solve for #x#.

#(3x-1)(x-2) = 0#

#3x-1 = 0# or #x-2 = 0#

#x = 1/3# or #x = 2#

The critical values are # x = 1/3# and #x = 2#.

Step 4. Identify the intervals.

The intervals to consider: (#-∞, +1/3#), (#1/3, 2#), and (#2, ∞#).

Step 5. Evaluate the intervals.

We pick a test number and evaluate the function and its sign at that number.

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Step 6. Create a sign chart for the function.

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The only intervals for which the signs are positive are.

Solution: #x < 1/3#or #x > 2#