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Question 1 of 4
Choose the number line that represents the inequality
2(x-1)≤62(x−1)≤6
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Representing Inequalities in the Number Line
Greater than or equal (≥≥)
First, make sure that only xx is on the left side
2(x-1)2(x−1) |
≤≤ |
66 |
2x-22x−2 |
≤≤ |
66 |
Expand |
2x-22x−2 +2+2 |
≤≤ |
66 +2+2 |
Add 22 to both sides |
2x2x |
≤≤ |
88 |
2x2x÷2÷2 |
≤≤ |
88÷2÷2 |
Divide both sides by 22 |
xx |
≤≤ |
44 |
The given inequality has a less than or equal to (≤≤) sign.
Hence, place a solid circle above 44 and attach an arrow pointing to the left to represent all values less than 44.
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Question 2 of 4
Choose the number line that represents the inequality
4(x+2)≥124(x+2)≥12
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Representing Inequalities in the Number Line
Greater than or equal (≥≥)
First, make sure that only xx is on the left side
4(x+2)4(x+2) |
≥≥ |
1212 |
4x+84x+8 |
≥≥ |
1212 |
Expand |
4x+84x+8 -8−8 |
≥≥ |
1212 -8−8 |
Subtract 88 from both sides |
4x4x |
≥≥ |
44 |
4x4x÷4÷4 |
≥≥ |
44÷4÷4 |
Divide both sides by 44 |
xx |
≥≥ |
11 |
The given inequality has a greater than or equal to (≥≥) sign.
Hence, place a solid circle above 11 and attach an arrow pointing to the right to represent all values greater than 11.
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Question 3 of 4
Choose the number line that represents the inequality
x-85≥-2x−85≥−2
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Representing Inequalities in the Number Line
Greater than or equal (≥≥)
First, make sure that only xx is on the left side
x-85x−85 |
≥≥ |
-2−2 |
|
x-85x−85×5×5 |
≥≥ |
-2−2×5×5 |
Multiply both sides by 55 |
|
x-8x−8 |
≥≥ |
-10−10 |
55=155=1 |
|
x-8x−8 +8+8 |
≥≥ |
-10−10 +8+8 |
Add 88 to both sides |
xx |
≥≥ |
-2−2 |
The given inequality has a greater than or equal to (≥≥) sign.
Hence, place a solid circle above -2−2 and attach an arrow pointing to the right to represent all values greater than -2−2.
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Question 4 of 4
Choose the number line that represents the inequality
1-2x31−2x3<<11
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Representing Inequalities in the Number Line
Greater than or equal (≥≥)
First, make sure that only xx is on the left side
1-2x31−2x3 |
<< |
11 |
|
1-2x31−2x3×3×3 |
<< |
11×3×3 |
Multiply both sides by 55 |
|
1-2x1−2x -1−1 |
<< |
33 -1−1 |
Subtract 11 from both sides |
-2x−2x ÷(-2)÷(−2) |
<< |
22 ÷(-2)÷(−2) |
Divide both sides by -2−2 |
xx |
>> |
-1−1 |
Flip the inequality |
The given inequality has a greater than (>>) sign.
Hence, place an empty circle above -1−1 and attach an arrow pointing to the right to represent all values greater than -1−1.