Solve the inequality \(2x - 3 > 5\) and \(3x + 2 < 14\) and express the solution as a single interval.
Answer
Since we want the solution that satisfies both inequalities, we need to find the intersection of the intervals \(x > 4\) and \(x < 4\). However, there is no value of x that is both greater than and less than 4, so the intersection is the empty set.
Step 1 ：First solve the inequality \(2x - 3 > 5\). Add 3 to both sides to get \(2x > 8\), then divide by 2 to get \(x > 4\).
Step 2 ：Next solve the inequality \(3x + 2 < 14\). Subtract 2 from both sides to get \(3x < 12\), then divide by 3 to get \(x < 4\).
Step 3 ：Since we want the solution that satisfies both inequalities, we need to find the intersection of the intervals \(x > 4\) and \(x < 4\). However, there is no value of x that is both greater than and less than 4, so the intersection is the empty set.
