Question

What are the solutions of the inequality? Check the solutions.

5(x – 4) < 10
(1 point)
Responses

x < –10
x < –10

x < 6
x < 6

x > –6
x > –6

x > 4

Answer 1

The solutions of the inequality are:

x < 6.
x > 4.

Checking the solutions:

For x = 5, 5(x - 4) < 10 becomes 5(5 - 4) < 10, which simplifies to 5 < 10. Since this statement is true, x = 5 is a valid solution.

For x = -7, 5(x - 4) < 10 becomes 5(-7 - 4) < 10, which simplifies to 5(-11) < 10 and -55 < 10. Since this statement is also true, x = -7 is a valid solution.

For x = 3, 5(x - 4) < 10 becomes 5(3 - 4) < 10, which simplifies to 5(-1) < 10 and -5 < 10. Since this statement is true, x = 3 is a valid solution.

Therefore, both x = 5 and x = -7 are solutions to the inequality. The solutions x < 6 and x > 4 are correct.