Solve.
[tex]\frac{30}{x}=6[/tex]
Answer (2)
Multiply both sides of the equation by x : 30 = 6 x .
Divide both sides by 6 to isolate x : x = 6 30 .
Simplify the fraction: x = 5 .
The solution to the equation is 5 .
Explanation
Understanding the Problem We are given the equation x 30 = 6 and our goal is to find the value of x that satisfies this equation.
Multiplying by x To solve for x , we can start by multiplying both sides of the equation by x . This gives us: x ⋅ x 30 = 6 ⋅ x Simplifying, we get: 30 = 6 x
Dividing by 6 Now, to isolate x , we divide both sides of the equation by 6: 6 30 = 6 6 x This simplifies to: x = 6 30
Simplifying the Fraction Finally, we simplify the fraction: x = 5 So, the solution to the equation is x = 5 .
Examples
Imagine you're baking a cake and the recipe calls for a certain ratio of flour to sugar. If you know you need 30 cups of batter and the ratio of flour to sugar should be 6:1, this problem helps you determine how many cups of sugar ( x ) you need. By solving the equation x 30 = 6 , you find that you need 5 cups of sugar. This type of proportional reasoning is essential in cooking, mixing solutions, and many other real-life scenarios where maintaining correct ratios is crucial.
To solve x 30 = 6 , we first eliminate the fraction by multiplying by x , yielding 30 = 6 x . Then, we isolate x by dividing both sides by 6, leading to the solution x = 5 . Thus, the final answer is 5 .
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