Compare the process of solving x-11+1<15 to that of solving x-1+1 >15.

Both inequalities involve simplifying expressions to isolate x . The first inequality, x − 11 + 1 < 15 , requires combining terms and then adding, resulting in x < 25 . The second inequality, 15"> x − 1 + 1 > 15 , simplifies directly to 15"> x > 15 , making it more straightforward.
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Answered by Anonymous | 2025-07-04

Simplify the first inequality: x − 11 + 1 < 15 becomes x − 10 < 15 .
Solve for x in the first inequality: x < 25 .
Simplify the second inequality: 15"> x − 1 + 1 > 15 becomes 15"> x > 15 .
Compare the processes: The first inequality requires an additional step to isolate x , while the second inequality is already in its simplest form. The solution to the first inequality is x < 25 and the solution to the second inequality is 15"> x > 15 .

Explanation

Understanding the Problem We are asked to compare the process of solving two inequalities: x − 11 + 1 < 15 and 15"> x − 1 + 1 > 15 .

Solving the First Inequality Let's simplify and solve the first inequality, x − 11 + 1 < 15 . First, combine the constants on the left side: x − 10 < 15 . To isolate x , add 10 to both sides of the inequality: x − 10 + 10 < 15 + 10 , which simplifies to x < 25 .

Solving the Second Inequality Now, let's simplify and solve the second inequality, 15"> x − 1 + 1 > 15 . The left side simplifies to 15"> x > 15 . So, the second inequality is already solved for x , and we have 15"> x > 15 .

Comparing the Processes Comparing the two processes, we see that both inequalities involve simplification. The first inequality, x − 11 + 1 < 15 , requires simplifying the left side and then adding 10 to both sides to isolate x . The second inequality, 15"> x − 1 + 1 > 15 , simplifies directly to 15"> x > 15 , so no further steps are needed to isolate x . The key difference is that the first inequality requires an additional step to isolate x , while the second inequality is already in its simplest form.


Examples
Understanding how to solve inequalities is crucial in many real-world scenarios. For instance, if you're budgeting your expenses, you might use an inequality to determine how much you can spend on entertainment each month while still covering your essential bills. Similarly, in science, inequalities can help define the range of acceptable values for experimental parameters to ensure accurate and safe results. Inequalities are also used in optimization problems to find the best possible solution within given constraints.

Answered by GinnyAnswer | 2025-07-04