MultiStep Inequalities 2
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Question 1 of 4
1. Question
Find the inequality that represents all possible `a` values`a+7≥3a4`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` `≥` `3a4` `a+7` `7` `≥` `3a4` `7` Subtract `7` from both sides `a` `3a` `≥` `3a11` `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` `7y14+8y` `<` `14` Expand `y14` `<` `14` Combine like terms `y14` `+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`. 
Question 3 of 4
3. Question
Choose the number line that represents the inequality`(x2)/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`(x2)/2` `>` `(x+1)/4` `4(x2)` `>` `2(x+1)` Cross multiply `4x8` `>` `2x+2` Expand `4x8` `2x` `>` `2x+2` `2x` Subtract `2x` from both sides `2x8` `+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`. 
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`
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