Question

Identify which values are solutions of the inequality 42 - 7 < -1.

a) -10
b) -8
c) -1
d) 0
e) 5
f) 10

Answer 1

The solution to the inequality 42 - 7x < -1 is any value greater than 6.14. Upon evaluating the given options, only f) 10 is greater than 6.14 and thus is the solution.

Step-by-step explanation:

To identify which values are solutions of the inequality 42 - 7x < -1, we can start by isolating the variable x. Following the steps below:

1. Subtract 42 from both sides of the inequality: -7x < -1 - 42.
2. Simplify the right side: -7x < -43.
3. Divide both sides by -7, remembering to reverse the inequality sign since we are dividing by a negative number: x > 43/7.
4. Simplify the fraction: x > 6.14.

Now we need to check which of the given values are greater than 6.14.

The only options from the provided list that are solutions to the inequality are:

• e) 5 (not a solution, as 5 is less than 6.14)
• f) 10 (is a solution, as 10 is greater than 6.14)

Therefore, the correct answer is f) 10.