Questions: What is the solution set of the equation below? x + 4 = 3x - 12 A. ∅ B. 5 E. 8 . 5,8

What is the solution set of the equation below?
 x + 4  = 3x - 12
A. ∅
B. 5
E. 8
. 5,8
Transcript text: What is the solution set of the equation below? \[ |x+4|=3 x-12 \] A. $\varnothing$ B. $\{5\}$ E. $\{8\}$ . $\{5,8\}$
failed

Solution

failed
failed

Solution Steps

Step 1: Understand the Absolute Value Equation

The equation is x+4=3x12 |x + 4| = 3x - 12 . An absolute value equation A=B |A| = B has two cases:

  1. A=B A = B
  2. A=B A = -B
Step 2: Solve Case 1 (x+4=3x12 x + 4 = 3x - 12 )

Set x+4=3x12 x + 4 = 3x - 12 and solve for x x : x+4=3x12 x + 4 = 3x - 12 Subtract x x from both sides: 4=2x12 4 = 2x - 12 Add 12 12 to both sides: 16=2x 16 = 2x Divide by 2 2 : x=8 x = 8

Step 3: Solve Case 2 (x+4=(3x12) x + 4 = -(3x - 12) )

Set x+4=3x+12 x + 4 = -3x + 12 and solve for x x : x+4=3x+12 x + 4 = -3x + 12 Add 3x 3x to both sides: 4x+4=12 4x + 4 = 12 Subtract 4 4 from both sides: 4x=8 4x = 8 Divide by 4 4 : x=2 x = 2

Step 4: Verify Solutions

For x=8 x = 8 : 8+4=3(8)12    12=12(Valid) |8 + 4| = 3(8) - 12 \implies 12 = 12 \quad \text{(Valid)}

For x=2 x = 2 : 2+4=3(2)12    6=6(Invalid) |2 + 4| = 3(2) - 12 \implies 6 = -6 \quad \text{(Invalid)}

Only x=8 x = 8 is valid.

Final Answer

The correct answer is C. {8} \boxed{\{8\}}

Was this solution helpful?
failed
Unhelpful
failed
Helpful