Compound Inequalities 2
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Question 1 of 4
1. Question
Choose the number line that represents the inequality`x≥1` OR `x``<``-2`Hint
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A compound inequality consists of two inequalities joined together by AND or OR.Plot `x≥``1` first.The given inequality has a greater than or equal to (`≥`) sign.Hence, place a solid circle above `1` and attach an arrow pointing to the right to represent all values greater than `1`.
Next, plot `x``<``-2`.The given inequality has a less than (`<`) sign.Hence, place an empty circle above `-2` and attach an arrow pointing to the left to represent all values less than `-2`.
Finally, combine the two number lines.
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Question 2 of 4
2. Question
Find the inequality that represents all possible `x` values`1``<``x+3≤9`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`1``<``x+3` `≤` `9` `1` `-3``<``x+3` `-3` `≤` `9` `-3` Subtract `3` from all sections `-2``<``x` `≤` `6` `-2``<``x≤6` -
Question 3 of 4
3. Question
Find the inequality that represents all possible `x` values`-6≤-x-5≤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≤-x-5` `≤` `2` `-6` `+5``≤-x-5` `+5` `≤` `2` `+5` Add `5` to all sections `-1` `times(-1)``≤-x` `times(-1)` `≤` `7` `times(-1)` Multiply all sections by `-1` `1≥x` `≥` `-7` Flip the inequality `-7≤x` `≤` `1` Place the lower value to the left `-7≤x≤1` -
Question 4 of 4
4. Question
Find the inequality that represents all possible `x` values`10``>``2-4x` AND `7-4x``>``-5`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 `10``>``2-4x` first.`10` `>` `2-4x` `10` `-2` `>` `2-4x` `-2` Subtract `2` from both sides `8``divide(-4)` `>` `-4x``divide(-4)` Divide both sides by `-4` `-2` `<` `x` Flip the inequality Next, solve for `7-4x``>``-5`.`7-4x` `>` `-5` `7-4x` `-7` `>` `-5` `-7` Subtract `7` from both sides `-4x``divide(-4)` `>` `-12``divide(-4)` Divide both sides by `-4` `x` `<` `3` Flip the inequality The two inequalities can be rewritten as:`-2` `<` `x` `<` `3` `-2``<``x``<``3`