Multi-Step Inequalities 1
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Question 1 of 4
1. Question
Choose the number line that represents the inequality`2(x-1)≤6`Hint
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Representing Inequalities in the Number Line
Greater than (`>`)
Greater than or equal (`≥`)
Less than (`<`)
Less than or equal (`≤`)
First, make sure that only `x` is on the left side`2(x-1)` `≤` `6` `2x-2` `≤` `6` Expand `2x-2` `+2` `≤` `6` `+2` Add `2` to both sides `2x` `≤` `8` `2x``divide2` `≤` `8``divide2` Divide both sides by `2` `x` `≤` `4` The given inequality has a less than or equal to (`≤`) sign.Hence, place a solid circle above `4` and attach an arrow pointing to the left to represent all values less than `4`.
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Question 2 of 4
2. Question
Choose the number line that represents the inequality`4(x+2)≥12`Hint
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Representing Inequalities in the Number Line
Greater than (`>`)Greater than or equal (`≥`)Less than (`<`)Less than or equal (`≤`)First, make sure that only `x` is on the left side`4(x+2)` `≥` `12` `4x+8` `≥` `12` Expand `4x+8` `-8` `≥` `12` `-8` Subtract `8` from both sides `4x` `≥` `4` `4x``divide4` `≥` `4``divide4` Divide both sides by `4` `x` `≥` `1` 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`.
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Question 3 of 4
3. Question
Choose the number line that represents the inequality`(x-8)/5≥-2`Hint
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Representing Inequalities in the Number Line
Greater than (`>`)Greater than or equal (`≥`)Less than (`<`)Less than or equal (`≤`)First, make sure that only `x` is on the left side`(x-8)/5` `≥` `-2` `(x-8)/5``times5` `≥` `-2``times5` Multiply both sides by `5` `x-8` `≥` `-10` `5/5=1` `x-8` `+8` `≥` `-10` `+8` Add `8` to both sides `x` `≥` `-2` The given inequality has a greater than or equal to (`≥`) sign.Hence, place a solid circle above `-2` and attach an arrow pointing to the right to represent all values greater than `-2`.
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Question 4 of 4
4. Question
Choose the number line that represents the inequality`(1-2x)/3``<``1`Hint
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Representing Inequalities in the Number Line
Greater than (`>`)Greater than or equal (`≥`)Less than (`<`)Less than or equal (`≤`)First, make sure that only `x` is on the left side`(1-2x)/3` `<` `1` `(1-2x)/3``times3` `<` `1``times3` Multiply both sides by `5` `1-2x` `-1` `<` `3` `-1` Subtract `1` from both sides `-2x` `divide(-2)` `<` `2` `divide(-2)` Divide both sides by `-2` `x` `>` `-1` Flip the inequality The given inequality has a greater than (`>`) sign.Hence, place an empty circle above `-1` and attach an arrow pointing to the right to represent all values greater than `-1`.