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3 years ago

What is the solution to the inequality? 5(x−2)<−3x+6

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

5 0

Answer:

x<2

Step-by-step explanation:

multiply 5 by the numbers inside the parenthesis

5x-10<-3x+6

add 10 to both sides

5x-10+10<-3x+6+10

simplify

5x<-3x+16

add 3x to both sides

5x+3x<-3x+16+3x

simplify

8x<16

divide by 8

8x/8 < 16/8

x<2

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$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$

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$\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{sin^2\theta-cos^2\theta}$

$\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}$

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$\dfrac{2sec^2\theta}{tan^2\theta-1}$

Left side = Right side <em>so proof is complete</em>

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3 years ago

Read 2 more answers