Multi-Step Inequalities 2
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Question 1 of 4
1. Question
Find the inequality that represents all possible `a` values`a+7≥3a-4`Hint
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If a negative value is multiplied to both sides of an inequality, the inequality flips.`-x``<``a` becomes `x``>``-a`First, make sure that only `a` is on the left side`a+7` `≥` `3a-4` `a+7` `-7` `≥` `3a-4` `-7` Subtract `7` from both sides `a` `-3a` `≥` `3a-11` `-3a` Subtract `3a` from both sides `-2a``divide(-2)` `≥` `-11``divide(-2)` Divide both sides by `-2` `a` `≤` `5 1/2` Flip the inequality `a≤5 1/2` -
Question 2 of 4
2. Question
Choose the number line that represents the inequality`-7(y+2)+8y``<``-14`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 `y` is on the left side`-7(y+2)+8y` `<` `-14` `-7y-14+8y` `<` `-14` Expand `y-14` `<` `-14` Combine like terms `y-14` `+14` `<` `-14` `+14` Add `14` to both sides `y` `<` `0` The given inequality has a less than (`<`) sign.Hence, place an empty circle above `0` and attach an arrow pointing to the left to represent all values less than `0`.
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Question 3 of 4
3. Question
Choose the number line that represents the inequality`(x-2)/2``>``(x+1)/4`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-2)/2` `>` `(x+1)/4` `4(x-2)` `>` `2(x+1)` Cross multiply `4x-8` `>` `2x+2` Expand `4x-8` `-2x` `>` `2x+2` `-2x` Subtract `2x` from both sides `2x-8` `+8` `>` `2` `+8` Add `8` to both sides `2x` `divide2` `>` `10` `divide2` Divide both sides by `2` `x` `>` `5` The given inequality has a greater than (`>`) sign.Hence, place an empty circle above `5` and attach an arrow pointing to the right to represent all values greater than `5`.
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Question 4 of 4
4. Question
Simplify`(3x)/5+2≤(2x)/5`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`(3x)/5+2` `≤` `(2x)/5` `((3x)/5+2)``times5` `≤` `((2x)/5)``times5` Multiply both sides by `5` `3x+10` `-2x` `≤` `2x` `-2x` Subtract `2x` from both sides `x+10` `-10` `≤` `0` `-10` Subtract `10` from both sides `x` `≤` `-10` `x≤-10`