Absolute Value Inequalities

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Separate into two inequalities: x + 3 > 8 or x + 3 < -8, which simplifies to x > 5 or x < -11.

It represents the values of x that are within 8 units of 0, leading to -8 < -8x < 8.

A compound inequality combines two inequalities, often using 'and' or 'or' to connect them.

The solution is -1 ≤ x ≤ 9, meaning x is between -1 and 9, inclusive.

Separate into two inequalities: x + 2 < 6 and x + 2 > -6.

It means r can take any value from -38 to 32, including the endpoints.

Draw a number line, shade to the left of -1 and to the right of 2, indicating that m can be in either region.

The 'and' indicates that both conditions must be true simultaneously, often leading to a range of values.

The solution is x < -4 or x > 4, meaning x is outside the interval [-4, 4].