Let's carefully solve the given equation step by step to identify the mistake that Asif made and determine the correct solution.
The original equation is:
[tex]\[ 6x - 2 = 3(x + 4) \][/tex]
Step 1: Distribute the 3 on the right side
[tex]\[ 6x - 2 = 3x + 12 \][/tex]
Asif's first mistake occurred in this step. He incorrectly wrote [tex]\( 3(x + 4) \)[/tex] as [tex]\( 3x + 7 \)[/tex]. The correct distributed form is [tex]\( 3x + 12 \)[/tex].
Step 2: Move all terms involving [tex]\( x \)[/tex] to one side and constants to the other side
Subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[ 6x - 3x - 2 = 12 \][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 3x - 2 = 12 \][/tex]
Add 2 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 3x = 12 + 2 \][/tex]
[tex]\[ 3x = 14 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{14}{3} \][/tex]
So the correct solution is:
[tex]\[ x = \frac{14}{3} \][/tex]
[tex]\[ x = 4.666666666666667 \][/tex]
Asif's mistake was in the distribution step. He incorrectly simplified [tex]\( 3(x + 4) \)[/tex] to [tex]\( 3x + 7 \)[/tex]. The correct simplification is [tex]\( 3x + 12 \)[/tex], leading to the correct answer of [tex]\( \frac{14}{3} \)[/tex] or approximately [tex]\( 4.666666666666667 \)[/tex].
