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

Jul 4, 2015

(-∞, 1/3) and (2, ∞)

#### Explanation:

$- 2 + 7 x - 3 {x}^{2} < 0$

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

Step 1. Write the inequality in standard form.

$- 3 {x}^{2} + 7 x - 2 < 0$

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

$3 {x}^{2} - 7 x + 2 > 0$

Step 3. Find the critical values.

Set $f \left(x\right) = 3 {x}^{2} - 7 x + 2 = 0$ and solve for $x$.

$\left(3 x - 1\right) \left(x - 2\right) = 0$

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

$x = \frac{1}{3}$ or $x = 2$

The critical values are $x = \frac{1}{3}$ and $x = 2$.

Step 4. Identify the intervals.

The intervals to consider: (-∞, +1/3), ($\frac{1}{3} , 2$), and (2, ∞).

Step 5. Evaluate the intervals.

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

Step 6. Create a sign chart for the function.

The only intervals for which the signs are positive are.

Solution: $x < \frac{1}{3}$or $x > 2$