What is the value of $x$ in the equation $-\frac{5}{8} x=-160$?
A. -256
B. -100
C. 100
D. 256
Answer (1)
Multiply both sides of the equation by − 5 8 to isolate x .
Calculate the product: x = − 160 × ( − 5 8 ) .
Simplify the expression: x = 5 1280 .
The value of x is 256 .
Explanation
Understanding the problem We are given the equation − 8 5 x = − 160 and we want to find the value of x .
Isolating x To isolate x , we need to multiply both sides of the equation by the reciprocal of − 8 5 , which is − 5 8 . So we have: x = − 160 × ( − 5 8 )
Calculating the value of x Now we perform the multiplication: x = − 160 × ( − 5 8 ) = 5 − 160 × − 8 = 5 1280 = 256
Final Answer Therefore, the value of x is 256.
Examples
Imagine you're baking a cake and need to adjust a recipe. If the original recipe calls for − 8 5 cups of sugar and you want the cake to be -160 times sweeter (in some arbitrary unit), you would need to calculate the new amount of sugar required. This problem demonstrates how to scale quantities using multiplication and division, ensuring the correct proportions are maintained in your adjusted recipe. Understanding such scaling is crucial in cooking, chemistry, and many other fields where precise measurements are essential.
