Question

Which is the best interpretation of the solution set for the compound inequality?

x - 1 < 2x + 4 or 3(x + 1) < 11

a) No solution
b) x > -10
c) x < 4
d) All real numbers

Answer 1

To solve the compound inequality, separate the inequalities, solve each one, and then combine them. The inequalities are joined by 'or', meaning any real number that satisfies either inequality is part of the solution set. Hence, the correct interpretation of the solution set is 'All real numbers'.

Step-by-step explanation:

Let's solve each part of the compound inequality separately and then interpret the solution set.

For the first inequality, x - 1 < 2x + 4, subtracting x from both sides gives us:

• -1 < x + 4
• -5 < x (after subtracting 4 from both sides)

Now let's solve the second inequality, 3(x + 1) < 11:

• 3x + 3 < 11
• 3x < 8 (after subtracting 3 from both sides)
• x < 8/3

Putting both solutions together:

• x > -5 (from the first inequality)
• x < 8/3 (from the second inequality)

Since the original inequalities are joined by 'or', the solution is the union of the two sets. Therefore, the correct answer is:

• d) All real numbers

Any real number is either greater than -5 or less than 8/3, satisfying at least one of the inequalities.