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Question 1 of 4
Choose the number line that represents the inequality
x≥1x≥1 OR xx<<-2−2
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A compound inequality consists of two inequalities joined together by AND or OR.
Plot x≥x≥11 first.
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.
Next, plot xx<<-2−2.
The given inequality has a less than (<<) sign.
Hence, place an empty circle above -2−2 and attach an arrow pointing to the left to represent all values less than -2−2.
Finally, combine the two number lines.
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Question 2 of 4
Find the inequality that represents all possible xx values
11<<x+3≤9x+3≤9
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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
11<<x+3x+3 |
≤≤ |
99 |
11 -3−3<<x+3x+3 -3−3 |
≤≤ |
99 -3−3 |
Subtract 33 from all sections |
-2−2<<xx |
≤≤ |
66 |
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Question 3 of 4
Find the inequality that represents all possible xx values
-6≤-x-5≤2−6≤−x−5≤2
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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≤-x-5−6≤−x−5 |
≤≤ |
22 |
-6−6 +5+5≤-x-5≤−x−5 +5+5 |
≤≤ |
22 +5+5 |
Add 55 to all sections |
-1−1 ×(-1)×(−1)≤-x≤−x ×(-1)×(−1) |
≤≤ |
77 ×(-1)×(−1) |
Multiply all sections by -1−1 |
1≥x1≥x |
≥≥ |
-7−7 |
Flip the inequality |
-7≤x−7≤x |
≤≤ |
11 |
Place the lower value to the left |
|
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Question 4 of 4
Find the inequality that represents all possible xx values
1010>>2-4x2−4x AND 7-4x7−4x>>-5−5
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A compound inequality consists of two inequalities joined together by AND or OR.
Solve the two inequalities seperately.
Solve for 1010>>2-4x2−4x first.
1010 |
>> |
2-4x2−4x |
1010 -2−2 |
>> |
2-4x2−4x -2−2 |
Subtract 22 from both sides |
88÷(-4)÷(−4) |
>> |
-4x−4x÷(-4)÷(−4) |
Divide both sides by -4−4 |
-2−2 |
<< |
xx |
Flip the inequality |
Next, solve for 7-4x7−4x>>-5−5.
7-4x7−4x |
>> |
-5−5 |
7-4x7−4x -7−7 |
>> |
-5−5 -7−7 |
Subtract 77 from both sides |
-4x−4x÷(-4)÷(−4) |
>> |
-12−12÷(-4)÷(−4) |
Divide both sides by -4−4 |
xx |
<< |
33 |
Flip the inequality |
The two inequalities can be rewritten as: