Which compound inequality is represented by the graph?
1 answer:
The compound inequality represented by the graph shown in the image below is 5 < x < 9
<h3>What is an equation?</h3>An equation is an expression that shows the relationship between two or more variables and numbers.
The image shown represents a compound inequality. It represents:
x > 5 and x < 9
The compound inequality represented by the graph shown in the image below is 5 < x < 9
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Step 1: Factor 
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite
as the sum of 
and 
Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.
</span>
<span>
Step 3: </span>Factor out the common term
Step 4: Solve for
1. Ask: When will
equal zero?
2. Answer: When
or 
3. <span>Solve each of the 2 equations above:
</span>
<span>
Step 5: </span>From the values of <span>above, we have these 3 intervals to test.
x = < -1/2
-1/2 < x < 2
x > 2
Step 6: P</span><span>ick a test point for each interval
</span>For the interval
Lets pick
Then, 
After simplifying, we get
, Which is false.
Drop this interval.
<span>
For this interval
Lets pick
. Then, 
. After simplifying, we get 
which is true. Keep this <span>interval.
For the interval </span>
Lets pick
Then, 
After simplifying, we get 
, Which is false. Drop this interval.
.Step 7: Therefore,
Done! :)</span>
1. <span> Multiply 2 by -2, which is -4.</span>
2. <span>Ask: Which two numbers add up to -3 and multiply to -4?
</span>3. <span>Answer: 1 and -4
</span>4. Rewrite
Step 2: <span>Factor out common terms in the first two terms, then in the last two terms.
</span>
<span>
Step 3: </span>Factor out the common term
Step 4: Solve for
1. Ask: When will
2. Answer: When
3. <span>Solve each of the 2 equations above:
</span>
<span>
Step 5: </span>From the values of
x = < -1/2
-1/2 < x < 2
x > 2
Step 6: P</span><span>ick a test point for each interval
</span>For the interval
Lets pick
After simplifying, we get
Drop this interval.
<span>
For this interval
Lets pick
For the interval </span>
Lets pick
.Step 7: Therefore,
Done! :)</span>