Question

solve the equation 4|3x - 12| = 36.

Explanation:

Step1: Divide both sides by 4

To isolate the absolute - value expression, we divide both sides of the equation \(4|3x - 12|=36\) by 4.
\(\frac{4|3x - 12|}{4}=\frac{36}{4}\)
This simplifies to \(|3x - 12| = 9\)

Step2: Set up two cases

By the definition of absolute value, if \(|A|=B\) (where \(B\geq0\)), then \(A = B\) or \(A=-B\). So for \(|3x - 12| = 9\), we have two cases:

• Case 1: \(3x-12 = 9\)
• Case 2: \(3x - 12=-9\)

Step3: Solve Case 1

For the equation \(3x-12 = 9\), we add 12 to both sides:
\(3x-12 + 12=9 + 12\)
\(3x=21\)
Then divide both sides by 3:
\(\frac{3x}{3}=\frac{21}{3}\)
\(x = 7\)

Step4: Solve Case 2

For the equation \(3x - 12=-9\), we add 12 to both sides:
\(3x-12 + 12=-9 + 12\)
\(3x = 3\)
Then divide both sides by 3:
\(\frac{3x}{3}=\frac{3}{3}\)
\(x = 1\)

Answer:

\(x = 1\) or \(x = 7\)