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Question 1 of 3
Find the inequality that represents all possible n values
−6<4n+10<2
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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 ÷4<4n ÷4 |
< |
−8 ÷4 |
Divide all sections by 4 |
| −4<n |
< |
−2 |
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Question 2 of 3
Choose the number line that represents the inequality
3x+5<2 OR 2x−7≥1
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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÷3 |
< |
−3÷3 |
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.
| 2x−7 |
≥ |
1 |
| 2x−7 +7 |
≥ |
1 +7 |
Add 7 to both sides |
| 2x÷2 |
≥ |
8÷2 |
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
Choose the number line that represents the inequality
y+11<8 OR −9y<−45
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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.
| −9y |
< |
−45 |
| −9y ÷(−9) |
< |
−45 ÷(−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.
