Question

Solve the inequality 4x - 18 < 56x - 16.

a) x < -1
b) -1 < x < 17
c) 1 < x
d) x > 5

Answer 1

To solve the inequality, manipulation of terms is required to isolate the variable. This results in the solution x > -1/26, which does not match the given multiple-choice answers.

Step-by-step explanation:

To solve the inequality 4x - 18 < 56x - 16, we need to isolate the variable x on one side. First, we subtract 4x from both sides of the inequality:

4x - 18 - 4x < 56x - 16 - 4x

-18 < 52x - 16

Next, we add 18 to both sides:

-18 + 18 < 52x - 16 + 18

0 < 52x + 2

Now, subtract 2 from both sides:

0 - 2 < 52x + 2 - 2

-2 < 52x

Finally, divide both sides by 52 to solve for x:

-2/52 < x

-1/26 < x, which simplifies to x > -1/26. However, none of the given options in the question correspond to this solution, suggesting there may be a mistake in the provided options or in the question itself.