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QuestionMathematics

What is the solution to $3 x^{2}+ 5 x>- 2$ ? A. $x<- 1$ or $x>-\frac{2}{3}$ B. $x \geq-\frac{2}{3}$ or $x<1$ C. $-\frac{2}{3} \leq x \leq 1$ D. $-\frac{2}{3}>x>- 1$
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Answer

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Step 1:
I'll solve this step by step using precise LaTeX formatting:

Step 2:
: Rearrange the inequality

• Start with $$3x^{2} + 5x > -2
• Rearrange to standard quadratic form: 3x^{2} + 5x + 2 > 0

Step 3:
: Solve the quadratic

• $$= 25 - 24 = 1
• Use the discriminant method

Step 4:
: Find roots

• Root 2: $$\frac{-5 - 1}{6} = -1
= \frac{- 5 \pm \sqrt{1}}{2(3)}

Step 5:
: Determine solution

• Therefore, $$x < -1$$ or $$x > -\frac{2}{3}
• Solution is outside the roots

Final Answer

A. x < - 1 or x > -\frac{2}{3}