Absolute Value Equations and Inequalities

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number.

Front

How do you solve an absolute value equation like |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does it mean when |x + 3| > 8?

Back

It means that the distance between x + 3 and 0 is greater than 8, leading to two possible inequalities: x + 3 > 8 or x + 3 < -8.

Front

What is the solution to |x + 3| > 8?

Back

x > 5 or x < -11.

Front

How do you solve an absolute value inequality like |m - 3| < b?

Back

To solve |m - 3| < b, you create a compound inequality: -b < m - 3 < b.

Front

What does |y - 4| ≥ 8 mean?

Back

It means that the distance between y and 4 is at least 8, leading to two possible inequalities: y - 4 ≥ 8 or y - 4 ≤ -8.

Front

What is the solution to |y - 4| ≥ 8?

Back

y ≤ -4 or y ≥ 12.

Front

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

Back

'And' means both conditions must be true at the same time, while 'or' means at least one condition must be true.

Front

How do you express the solution to r in the inequality r ≥ -38 and r ≤ 32?

Back

The solution can be expressed as -38 ≤ r ≤ 32.

Front

What is the solution to the equation |2x + 9| = 15?

Back

x = 3 or x = -12.