Question

Since \(x-3<5\) and \(x<8\) have the same solution, they are \(\underline{?}\) inequalities.

Short answer

The two inequalities are equivalent inequalities.

Step-by-step solution

Step 1. Solve the inequalities

We begin by solving both inequalities individually. For \(x-3<5\), we'll add 3 to both sides, yielding \(x<8\). As for \(x<8\), it is already solved, and no further modifications are needed.

Step 2. Comparison of the results

We can see from step 1 that the two inequalities \(x-3<5\) and \(x<8\) both become \(x<8\) when solved. This tells us that they are equivalent to each other in terms of solutions.

Step 3. Classify the inequalities

Our examination in step 2 showed that the two inequalities are having the same solution. When two inequalities have the same solution, it's understood that they are equivalent inequalities.