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3 years ago

10 POINTS Solve the following inequality. 4x-1> -9

Mathematics

1 answer:

hodyreva [135]3 years ago

6 0

Answer:

x > −2

Step-by-step explanation:

~Solve~

Let's solve your inequality step-by-step.

4x−1>−9

Step 1: Add 1 to both sides.

4x−1+1>−9+1

4x>−8

Step 2: Divide both sides by 4.

−8

x>−2

<u>Answer:</u>

x>−2

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$4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\$

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