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Question 1 of 3
Find the inequality that represents all possible nn values
-6−6<<4n+104n+10<<22
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A compound inequality consists of two inequalities joined together by AND or OR.
First, make sure that xx is left alone in the middle
| -6−6<<4n+104n+10 |
<< |
22 |
| -6−6 -10−10<<4n+104n+10 -10−10 |
<< |
22 -10−10 |
Subtract 1010 from all sections |
| -16−16 ÷4÷4<<4n4n ÷4÷4 |
<< |
-8−8 ÷4÷4 |
Divide all sections by 44 |
| -4−4<<nn |
<< |
-2−2 |
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Question 2 of 3
Choose the number line that represents the inequality
3x+53x+5<<22 OR 2x-7≥12x−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+53x+5<<22 first.
| 3x+53x+5 |
<< |
22 |
| 3x+53x+5 -5−5 |
<< |
22 -5−5 |
Subtract 55 from both sides |
| 3x3x÷3÷3 |
<< |
-3−3÷3÷3 |
Divide both sides by 33 |
| xx |
<< |
-1−1 |
The given inequality has a less than (<<) sign.
Hence, place a empty circle above -1−1 and attach an arrow pointing to the left to represent all values less than -1−1.
Next, solve for 2x-7≥12x−7≥1.
| 2x-72x−7 |
≥≥ |
11 |
| 2x-72x−7 +7+7 |
≥≥ |
11 +7+7 |
Add 77 to both sides |
| 2x2x÷2÷2 |
≥≥ |
88÷2÷2 |
Divide both sides by 22 |
| xx |
≥≥ |
44 |
The given inequality has a greater than or equal to (≥≥) sign.
Hence, place a solid circle above 44 and attach an arrow pointing to the right to represent all values greater than 9595.
Finally, combine the two number lines.
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Question 3 of 3
Choose the number line that represents the inequality
y+11y+11<<88 OR -9y−9y<<-45−45
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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+11y+11<<88 first.
| y+11y+11 |
<< |
88 |
| y+11y+11 -11−11 |
<< |
88 -11−11 |
Subtract 1111 from both sides |
| yy |
<< |
-3−3 |
The given inequality has a less than (<<) sign.
Hence, place a empty circle above -3−3 and attach an arrow pointing to the left to represent all values less than -3−3.
Next, solve for -9y−9y<<-45−45.
| -9y−9y |
<< |
-45−45 |
| -9y−9y ÷(-9)÷(−9) |
<< |
-45−45 ÷(-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.
