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Absolute Value Inequalities

In this video, we will be learning how to solve Absolute Value Inequalities. Remember to graph your inequalities!

When removing absolute value brackets, remember to flip the inequality sign and negate the other side of the inequality!

For Example:

|2x-8|+8\geq14

|2x-8|+8-8\geq14-8\leftarrow Subtract 8 from both sides to isolate the quantities in the absolute value brackets

|2x-8|\geq6\leftarrow Now remove the absolute value brackets and separate the equation into 2 cases as shown below

2x-8\geq6                                          2x-8\leq-6

2x-8+8\geq6+8                         2x-8+8\leq-6+8

\frac{2x}{2}\geq\frac{14}{2}                                                 \frac{2x}{2}\leq\frac{2}{2}

x\geq7                                                      x\leq1

abs ineq