Solving Absolute Value Inequalities and Equations

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on a number line.

Front

How do you solve the inequality |x - 5| < 3?

Back

To solve |x - 5| < 3, split it into two inequalities: -3 < x - 5 < 3. This simplifies to 2 < x < 8.

Front

What does it mean when |x| ≥ a?

Back

It means that x is either greater than or equal to a or less than or equal to -a.

Front

Solve the inequality |p + 3| ≥ 10.

Back

p ≤ -13 or p ≥ 7.

Front

What is the solution to the inequality -8x < 48?

Back

x > -6.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Write the equation in point-slope form for the line through (4, -7) with slope -1/4.

Back

y + 7 = -1/4(x - 4).

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line passing through the points (3, -1) and (7, 2)?

Back

The slope is 3/4.