Inequalities 11122 Q

Front

What is an absolute value inequality?

Back

An inequality that involves the absolute value of a variable, expressing a distance from a point on the number line.

Front

How do you solve |x - a| > b?

Back

Split into two cases: x - a > b or x - a < -b.

Front

How do you solve |x - a| < b?

Back

Split into two cases: -b < x - a < b, which simplifies to a - b < x < a + b.

Front

What does the solution |x - 2| > 3 represent?

Back

x < -1 or x > 5.

Front

What does the solution |x + 3| ≤ 2 represent?

Back

-5 ≤ x ≤ -1.

Front

What is the difference between 'and' and 'or' in inequalities?

Back

'And' means both conditions must be true; 'or' means at least one condition must be true.

Front

What is the solution to the inequality -|−2r − 1| = 11?

Back

No Solution, because the left side is always non-positive.

Front

How do you graph the solution of an inequality?

Back

Use a number line, shading the region that satisfies the inequality and using open/closed circles for boundaries.

Front

What does the notation x < a mean?

Back

x is less than a, meaning x can take any value to the left of a on the number line.

Front

What does the notation x ≥ a mean?

Back

x is greater than or equal to a, meaning x can take any value to the right of a, including a.