Compound Inequalities 3
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Question 1 of 3
1. Question
Find the inequality that represents all possible `n` values`-6``<``4n+10``<``2`Hint
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A compound inequality consists of two inequalities joined together by AND or OR.First, make sure that `x` is left alone in the middle`-6``<``4n+10` `<` `2` `-6` `-10``<``4n+10` `-10` `<` `2` `-10` Subtract `10` from all sections `-16` `divide4``<``4n` `divide4` `<` `-8` `divide4` Divide all sections by `4` `-4``<``n` `<` `-2` `-4``<``n``<``-2` -
Question 2 of 3
2. Question
Choose the number line that represents the inequality`3x+5``<``2` OR `2x-7≥1`Hint
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A compound inequality consists of two inequalities joined together by AND or OR.Solve the two inequalities seperately.Solve for `3x+5``<``2` first.`3x+5` `<` `2` `3x+5` `-5` `<` `2` `-5` Subtract `5` from both sides `3x``divide3` `<` `-3``divide3` Divide both sides by `3` `x` `<` `-1` The given inequality has a less than (`<`) sign.Hence, place a empty circle above `-1` and attach an arrow pointing to the left to represent all values less than `-1`.
Next, solve for `2x-7≥1`.`2x-7` `≥` `1` `2x-7` `+7` `≥` `1` `+7` Add `7` to both sides `2x``divide2` `≥` `8``divide2` Divide both sides by `2` `x` `≥` `4` The given inequality has a greater than or equal to (`≥`) sign.Hence, place a solid circle above `4` and attach an arrow pointing to the right to represent all values greater than `95`.
Finally, combine the two number lines.
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Question 3 of 3
3. Question
Choose the number line that represents the inequality`y+11``<``8` OR `-9y``<``-45`Hint
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A compound inequality consists of two inequalities joined together by AND or OR.Solve the two inequalities seperately.Solve for `y+11``<``8` first.`y+11` `<` `8` `y+11` `-11` `<` `8` `-11` Subtract `11` from both sides `y` `<` `-3` The given inequality has a less than (`<`) sign.Hence, place a empty circle above `-3` and attach an arrow pointing to the left to represent all values less than `-3`.
Next, solve for `-9y``<``-45`.`-9y` `<` `-45` `-9y` `divide(-9)` `<` `-45` `divide(-9)` Divide both sides by `-9` `y` `>` `5` Flip the inequality The given inequality has a greater than (`>`) sign.Hence, place a solid circle above `5` and attach an arrow pointing to the right to represent all values greater than `5`.
Finally, combine the two number lines.