Example Card: Isolating the Absolute-Value Expression

Sometimes the absolute value part isn't by itself. Let's see how to clear away the clutter first before solving.

Example Problem Solve the equation $3|x 4| = 45$.

Step by Step 1. To begin, we must isolate the absolute value expression. 2. Use the Division Property of Equality to divide both sides by 3. $$ \frac{3|x 4|}{3} = \frac{45}{3} $$ 3. Simplify the equation. $$ |x 4| = 15 $$ 4. Now that the absolute value is isolated, write $|x 4|=15$ as two equations. $$ x 4 = 15 \quad \text{or} \quad x 4 = 15$$ 5. Solve the first equation by adding 4 to both sides. $$ x = 19 $$ 6. Solve the second equation by adding 4 to both sides. $$ x = 11 $$ 7. The final solution is the set of both values. $$ \{19, 11\} $$.