Solving Inequalities Flashcards

< means 'less than', > means 'greater than', ≤ means 'less than or equal to', and ≥ means 'greater than or equal to'.

To solve a linear inequality, treat it like an equation: perform the same operation on both sides, but remember to reverse the inequality sign if multiplying or dividing by a negative number.

Inequalities can be represented on a number line. Use an open circle for < or > and a closed circle for ≤ or ≥.

When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality sign.

A compound inequality involves two inequalities joined by 'and' or 'or'. For example, -2 ≤ x < 5 means x is between -2 and 5, including -2 but not 5.

Substitute a value into the inequality to check if it satisfies the inequality.

Clear the fractions by multiplying through by the denominator (if positive). If the denominator is negative, reverse the inequality sign.

For inequalities like y > 2x + 1, shade the region above the line y = 2x + 1. Use a dashed line for > or < and a solid line for ≥ or ≤.

The solution to two inequalities joined by 'and' is the overlap of their solutions. For example, x > 1 and x ≤ 4 means 1 < x ≤ 4.

The solution to two inequalities joined by 'or' is the combined region of their solutions. For example, x < -1 or x > 3 means x is less than -1 or greater than 3.