Question

∣8x+4v∣<28

a. x<3
b. x>−5
c. −8d. x>7

Answer 1

The inequality involving the absolute value is solved by considering both the positive and negative cases of the expression inside the absolute value. As 'v' is not defined in the options provided, we can't match the inequality's solution exactly to any of the options. The process demonstrates how to handle absolute values within inequalities.

Step-by-step explanation:

The inequality √8x+4v√ < 28 can be solved by looking at both the positive and negative cases of the absolute value expression.

For the positive case:

1. 8x + 4v < 28
2. 8x < 28 - 4v (assuming v is a constant and subtracting 4v from both sides)
3. x < 3.5 - 0.5v (dividing both sides by 8)

For the negative case:

1. -(8x + 4v) < 28
2. -8x - 4v < 28
3. -8x < 28 + 4v (adding 4v to both sides)
4. x > -3.5 - 0.5v (dividing both sides by -8 and flipping the inequality because of dividing by a negative number)

Since the variable 'v' is not defined in the provided options, we cannot directly match the solution to options (a), (b), (c), or (d). None of the options provided correspond exactly to the derived solution.

However, this process illustrates how to solve inequalities involving absolute values by considering both cases where the expression inside the absolute value is positive and when it is negative.