Find the smaller solution of the equation 3|2x - 5| = 12.

Find the smaller solution of the equation 3|2x - 5| = 12.

• A. -4.5
• B. -0.5
• C. 4.5
• D. 0.5

Answer: (D)

Absolute-value equations give two possibilities because the inside can be positive or negative and still yield the same absolute value. Start by isolating the absolute value: divide both sides by 3 to get |2x - 5| = 4. Now the inside must be either 4 or -4. Solve each case: 2x - 5 = 4 leads to x = 9/2 = 4.5, and 2x - 5 = -4 leads to x = 1/2 = 0.5. The two solutions are 4.5 and 0.5, and the smaller one is 0.5. Checking with x = 0.5 gives |2(0.5) - 5| = |1 - 5| = 4, and 3·4 = 12, which matches the equation.

Absolute-value equations give two possibilities because the inside can be positive or negative and still yield the same absolute value. Start by isolating the absolute value: divide both sides by 3 to get |2x - 5| = 4. Now the inside must be either 4 or -4. Solve each case: 2x - 5 = 4 leads to x = 9/2 = 4.5, and 2x - 5 = -4 leads to x = 1/2 = 0.5. The two solutions are 4.5 and 0.5, and the smaller one is 0.5. Checking with x = 0.5 gives |2(0.5) - 5| = |1 - 5| = 4, and 3·4 = 12, which matches the equation.