b. [tex]$\frac{-2}{x}=\frac{19}{8}$[/tex]
Answer (2)
Cross-multiply the equation x − 2 = 8 19 to get − 2 × 8 = 19 × x .
Simplify the equation to − 16 = 19 x .
Divide both sides by 19 to isolate x : x = 19 − 16 .
The solution is − 19 16 .
Explanation
Understanding the Problem We are given the equation x − 2 = 8 19 . Our goal is to find the value of x that satisfies this equation.
Cross-Multiplication To solve for x , we can use cross-multiplication. This means multiplying the numerator of the first fraction by the denominator of the second fraction, and setting it equal to the product of the denominator of the first fraction and the numerator of the second fraction: − 2 × 8 = 19 × x
Simplifying the Equation Now, we simplify the equation: − 16 = 19 x
Isolating x To isolate x , we divide both sides of the equation by 19: 19 − 16 = 19 19 x This simplifies to: x = 19 − 16
Final Answer Therefore, the value of x that satisfies the equation is − 19 16 .
Examples
Imagine you're scaling a recipe. If the original recipe calls for a certain amount of an ingredient, and you want to make a smaller or larger batch, you can use proportions to find the new amount needed. For example, if a recipe uses x 2 cups of flour and you want to adjust the recipe so that it uses 8 19 of the original amount, solving for x will tell you how much flour you need to use in your adjusted recipe. This is a practical application of solving proportions in everyday life.
The solution to the equation x − 2 = 8 19 is x = − 19 16 . We found this by cross-multiplying and isolating x . Thus, the final answer is − 19 16 .
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