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Question 1 of 3
Choose the number line that represents the inequality
4m+5-3m≥-94m+5−3m≥−9
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Representing Inequalities in the Number Line
Greater than or equal (≥≥)
First, make sure that only mm is on the left side
| 4m+5-3m4m+5−3m |
≥≥ |
-9−9 |
| m+5m+5 |
≥≥ |
-9−9 |
Combine like terms |
| m+5m+5 -5−5 |
≥≥ |
-9−9 -5−5 |
Subtract 55 from both sides |
| mm |
≥≥ |
-14−14 |
The given inequality has a greater than or equal to (≥≥) sign.
Hence, place a solid circle above -14−14 and attach an arrow pointing to the right to represent all values greater than -14−14.
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Question 2 of 3
Find the inequality that represents all possible mm values
-m10−m10>>1212
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If a negative value is multiplied or divided to both sides of an inequality, the inequality flips.
-x−x<<aa becomes xx>>-a−a
First, make sure that only mm is on the left side
| m10m10 |
>> |
1212 |
|
| -m10−m10×10×10 |
>> |
1212×10×10 |
Multiply both sides by 1010 |
|
| -m−m |
>> |
102102 |
1010=11010=1 |
|
| -m−m×(-1)×(−1) |
>> |
55×(-1)×(−1) |
Multiply both sides by -1−1 |
| mm |
<< |
-5−5 |
Flip the inequality |
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Question 3 of 3
Find the inequality that represents all possible tt values
3t83t8<<-540−540
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If a negative value is multiplied or divided to both sides of an inequality, the inequality flips.
-x−x<<aa becomes xx>>-a−a
First, make sure that only mm is on the left side
| 3t83t8 |
<< |
-540−540 |
|
| 3t83t8×83×83 |
<< |
-540−540×83×83 |
Multiply both sides by 8383 |
|
| tt |
<< |
-40120−40120 |
8×38×3=18×38×3=1 |
|
| tt |
<< |
-13−13 |
Simplify |
