$-18<2c-10<0$
$c \in$ $\square$ (Enter your answer in intervals; or enter DNE if no solution exists)
Answer (2)
Add 10 to all parts of the inequality: − 18 + 10 < 2 c − 10 + 10 < 0 + 10 , which simplifies to − 8 < 2 c < 10 .
Divide all parts of the inequality by 2: − 8/2 < 2 c /2 < 10/2 , which simplifies to − 4 < c < 5 .
Express the solution as an interval: c ∈ ( − 4 , 5 ) .
The solution to the inequality is: ( − 4 , 5 )
Explanation
Understanding the Inequality We are given the inequality − 18 < 2 c − 10 < 0 and we want to find the interval for c that satisfies this inequality.
Isolating the Term with c First, we add 10 to all parts of the inequality to isolate the term with c :
− 18 + 10 < 2 c − 10 + 10 < 0 + 10 This simplifies to: − 8 < 2 c < 10
Solving for c Next, we divide all parts of the inequality by 2 to solve for c :
2 − 8 < 2 2 c < 2 10 This simplifies to: − 4 < c < 5
Finding the Interval Therefore, the solution is the interval ( − 4 , 5 ) .
Examples
Understanding inequalities like this helps in various real-life situations. For example, if you're planning a road trip and want to keep your travel time within a certain range, you can use inequalities to calculate the possible speeds you need to maintain. Or, if you're managing a budget, inequalities can help you determine how much you can spend on different items while staying within your financial limits. These mathematical tools are essential for making informed decisions and managing constraints effectively.
The solution to the inequality − 18 < 2 c − 10 < 0 is c ∈ ( − 4 , 5 ) . This was found by isolating c through adding and dividing. The final answer represents the interval of values for c that satisfy the inequality.
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