Q:

# which of the following is the solution to |10x|&gt;-2

Accepted Solution

A:
Let's reason through it.We are given the inequality that says, in English, that the absolute value of ten times x is greater than -2.Let's consider three cases:x is negative- When x is negative the number in the absolute value will be negative. But because it is inside the absolute value, the number becomes positive. Therefore, for any x that is negative (however small or large), the left side will be positive. Any positive value (however small) is greater than a negative value, so the inequality is satisfied in this case.x is positive- When x is positive, the number inside the absolute value will be positive. The absolute value of a positive number is itself, so the left hand side will be positive again. Then, for all positive values of x (however small or large), the inequality will be satisfied because any positive value is larger than -2.x is zero- Even in the case of zero, when the left hand side will be zero, the equality is satisfied. This is because zero is greater than -2. If this doesn't immediately make sense, imagine the two numbers on the number line. 0 is to the right of -2, so it is larger.Since we cannot find a value for x that does not satisfy the inequality, the solution to the inequality is all values of x. See the attached image.