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In Mathematics / High School | 2025-07-03

Which value of $w$ makes $14=11+\frac{w}{8} \cdot 6$ a true statement?

Choose 1 answer:
A. $w=1$
B. $w=4$
C. $w=16$
D. $w=24

Asked by dylane0812

Answer (2)

Subtract 11 from both sides: 14 − 11 = 8 w ​ \t ⋅ 6 which simplifies to 3 = 8 w ​ \t ⋅ 6 .
Multiply both sides by 8: 3 \t ⋅ 8 = w \t ⋅ 6 which simplifies to 24 = 6 w .
Divide both sides by 6: 6 24 ​ = w .
Simplify to find the value of w : w = 4 ​ .

Explanation

Understanding the problem We are given the equation 14 = 11 + 8 w ​ \t ⋅ 6 and we need to find the value of w that makes this equation true.

Isolating the term with w First, subtract 11 from both sides of the equation to isolate the term with w : 14 − 11 = 8 w ​ \t ⋅ 6

Simplifying the equation Simplify the left side of the equation: 3 = 8 w ​ \t ⋅ 6

Eliminating the fraction To get rid of the fraction, multiply both sides of the equation by 8: 3 \t ⋅ 8 = 8 w ​ \t ⋅ 6 \t ⋅ 8

Further simplification Simplify both sides of the equation: 24 = w \t ⋅ 6

Solving for w Now, divide both sides by 6 to solve for w :
6 24 ​ = 6 w \t ⋅ 6 ​

Finding the value of w Simplify to find the value of w :
w = 4

Conclusion Therefore, the value of w that makes the equation true is 4.


Examples
Imagine you're baking a cake and need to adjust a recipe. The equation 14 = 11 + 8 w ​ \t ⋅ 6 is like figuring out how much of an ingredient ( w ) to add. If you know the total sweetness you want (14) and the base sweetness (11), this equation helps you calculate the exact amount of the ingredient ( w ) needed to reach the desired sweetness. Solving such equations is crucial in cooking, chemistry, and any field where precise measurements are essential to achieve a desired outcome.

Answered by GinnyAnswer | 2025-07-03

The value of w that makes the equation true is 4. This is found by isolating w through algebraic manipulation of the equation. Therefore, the correct answer is option B, w = 4 .
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Answered by Anonymous | 2025-07-04

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