Question

How do you solve and graph the compound inequality `3x > 3` or `5x < 2x - 3` ?

Answer 1

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Solution:

`color(red)[(x>1) or (x < -1)`

Interval Notation:

`color(red)((-oo, -1) uu (1,oo)`

Explanation:

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We are given the inequality expression:

`color(blue)(3x > 3 or 5x < 2x - 3`

Since the `color(red)(Or` operator is used, we will use `color(red)(uu` in our final solution.

Solve the inequality expressions separately:

`color(blue)(3x>3`

Divide both the sides of the inequity by `color(red)(3`

`(3x)/3>3/3`

`(cancel 3x)/cancel 3>3/3`

`color(blue)(x > 1` ... Res.1

`color(blue)(5x < 2x - 3`

Subtract `color(red)(2x` from both sides of the inequality.

`5x-2x < 2x - 3-2x`

`5x-2x < cancel (2x) - 3-cancel(2x)`

`3x<-3`

Divide both sides of the inequality by `color(red)(3`

`(3x)/3<-3/3`

`(cancel 3x)/cancel 3<-3/3`

`color(blue)(x<-1` ... Res.2

Hence, the final solutions:

`color(red)[(x>1) or (x < -1)`

Interval Notation:

`color(red)((-oo, -1) uu (1,oo)`

Represent the solution on a graph:

Dotted Lines on the graph indicate values that are NOT part of the Solution Set.

Hope it helps.