Question
Save the inequality, and plot the solftion on real number
Ine
Ine
Ask by Gardner Lawson. in the United Arab Emirates
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There is no solution to the inequality, so the answer is the empty set: ∅.
Solution
We are given the chain inequality
We will break this into two separate inequalities and solve each.
Step 1. Solve the left inequality
First, expand the right side:
So, the inequality becomes:
Now, add
Subtract 5 from both sides:
Divide by 6:
Step 2. Solve the right inequality
Again, expand the left side:
Thus, the inequality becomes:
Add
Add 10 to both sides:
Divide by 9:
Step 3. Combine the results
The system requires:
No real number satisfies both conditions simultaneously. Therefore, the solution set is the empty set:
Step 4. Plot on the real number line
Since there is no solution, the plot on the real number line is empty (i.e., there is no
Thus, the final answer is:
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Explain 
Simplify this solution Bonus Knowledge
To solve the inequality
First, simplify the left part
- Expand
to get . - Now the inequality becomes
. - Solving this leads to
or .
Next, simplify the right part
- We already found
. - Now, the inequality becomes
. - This simplifies to
, or , which gives us .
Now we know that:
- For the first part, we have
. - For the second part, we have
.
Both inequalities cannot be true simultaneously, so the solution to the original compound inequality has no feasible solutions, and we cannot plot it on the real number line as there are no common values for
So, let’s break out the graph! You would typically illustrate it with an empty line - no shading, just a clear space to show that there is “nothing” in between
