Inequalities with Algebraic Expressions

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Jason
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ex. a

:?: What is the answer to the inequality? How is it expressed in interval notation?

\(5x > 10\)

\(x > \dfrac{10}{5}\)

\(x > 2\)

\((2 , \infty)\)
For ex. a, the interval notion above shows a left parentheses, not a bracket, because 2 is not part of the interval which stretches right from 2 and into infinity.
:!: Not Shown on Post

Interval for ex. a is represented by arrow going right from 2 with a clear circle on 2 meaning that 2 is not on the interval


ex. b.

:?: What is the answer to the inequality? How is it expressed in interval notation?
:!: Dividing or multiplying both sides by negative numbers switches the inequality sign.
\(-4x < 2\)

\(x > -\dfrac{2}{4} \)

\(x > -\dfrac{1}{2}\)

\(-\dfrac{1}{2} = -0.50\)

\((-0.50, \infty)\)
:!: Not Shown on Post

Interval for ex. b is shown as arrow going right from -0.50 to infinity with a clear circle on -0.50, showing that -0.50 is not on the interval.
 

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