What value of [tex]$x$[/tex] makes the following equation true?
[tex]\frac{3}{4}(7+x)=12[/tex]
A. 2
B. [tex]$6 \frac{1}{4}$[/tex]
C. 9
D. [tex]$17 \frac{1}{4}$[/tex]
Answer (2)
Multiply both sides of the equation by 3 4 : 7 + x = 12 × 3 4 .
Simplify the right side: 7 + x = 16 .
Subtract 7 from both sides: x = 16 − 7 .
Calculate the value of x : x = 9 . The value of x is 9 .
Explanation
Understanding the Problem We are given the equation 4 3 ( 7 + x ) = 12 and we need to find the value of x that makes this equation true.
Isolating the Term (7+x) To solve for x , we first multiply both sides of the equation by 3 4 to isolate the term ( 7 + x ) :
3 4 × 4 3 ( 7 + x ) = 12 × 3 4 7 + x = 12 × 3 4
Simplifying the Right Side Now, we simplify the right side of the equation: 7 + x = 3 12 × 4 7 + x = 3 48 7 + x = 16
Isolating x Next, we subtract 7 from both sides of the equation to isolate x :
7 + x − 7 = 16 − 7 x = 16 − 7
Calculating x Finally, we calculate the value of x :
x = 9 So, the value of x that makes the equation true is 9.
Examples
Imagine you're baking a cake and need to adjust a recipe. If 4 3 of the original recipe (7 ounces of flour plus an unknown amount x ) equals 12 ounces of batter, this problem helps you determine the exact amount of the unknown ingredient x needed to achieve the desired batter consistency. This type of algebraic problem is useful in scaling recipes, adjusting mixtures, or calculating quantities in various real-life scenarios.
The value of x that makes the equation true is 9 , which is answer option C.
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