Inequalities and Absolute Value Equations

Inequalities

Multiply or divide by a negative

a < b and c < 0 \Rightarrow a c > b c and \frac{a}{c} > \frac{b}{c}

Absolute value equation

| a x + b | = c \Leftrightarrow a x + b = c or a x + b = - c

c ≥ 0

Less than (and)

| a x + b | < c \Leftrightarrow - c < a x + b < c

c > 0

Greater than (or)

| a x + b | > c \Leftrightarrow a x + b > c or a x + b < - c

c > 0

Absolute value function

y = a | x - h | + k

vertex (h, k), axis x = h

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