What is the value of $x$ in the equation below?
$\frac{1}{3}(12 x-24)=16$
A. 2
B. 6
C. 8
D. 10
Answer (2)
Multiply both sides of the equation by 3: 12 x − 24 = 48 .
Add 24 to both sides: 12 x = 72 .
Divide both sides by 12: x = 6 .
The value of x is 6 .
Explanation
Understanding the Problem We are given the equation 3 1 ( 12 x − 24 ) = 16 and we want to find the value of x .
Eliminating the Fraction First, we multiply both sides of the equation by 3 to eliminate the fraction: 3 × 3 1 ( 12 x − 24 ) = 3 × 16 12 x − 24 = 48
Isolating the x Term Next, we add 24 to both sides of the equation to isolate the term with x : 12 x − 24 + 24 = 48 + 24 12 x = 72
Solving for x Finally, we divide both sides of the equation by 12 to solve for x : 12 12 x = 12 72 x = 6
Final Answer Therefore, the value of x is 6.
Examples
Imagine you're baking a cake and need to adjust the recipe. If 3 1 of the original recipe (represented by 12 x − 24 ) should equal 16 ounces of flour, solving this equation helps you determine the correct amount of the key ingredient, x . This type of problem is useful in scaling recipes, managing budgets, or adjusting any formula where proportional relationships are important. By understanding how to solve for x , you can accurately modify quantities in various real-life scenarios.
To solve the equation 3 1 ( 12 x − 24 ) = 16 , we find that by eliminating the fraction and isolating x , the solution is x = 6 . Hence, the answer is 6. The correct choice among the options provided is B. 6.
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