Solve [tex]\frac{1}{24} m-\frac{2}{3}=\frac{3}{4}[/tex] for [tex]m[/tex].
A. [tex]m=-12[/tex]
B. [tex]m=34[/tex]
C. [tex]m=36[/tex]
D. [tex]m=12[/tex]
Answer (2)
Add 3 2 to both sides of the equation: 24 1 m = 4 3 + 3 2 .
Find a common denominator and add the fractions: 24 1 m = 12 17 .
Multiply both sides by 24 to isolate m : m = 12 17 × 24 .
Simplify to find the value of m : m = 34 .
Explanation
Isolating the term with m We are given the equation 24 1 m − 3 2 = 4 3 . Our goal is to isolate m on one side of the equation to find its value. Let's start by adding 3 2 to both sides of the equation.
Adding the fractions Adding 3 2 to both sides, we get: 24 1 m = 4 3 + 3 2 To add the fractions on the right side, we need a common denominator. The least common multiple of 4 and 3 is 12. So, we rewrite the fractions with the common denominator: 24 1 m = 4 × 3 3 × 3 + 3 × 4 2 × 4 24 1 m = 12 9 + 12 8 Now, we can add the fractions: 24 1 m = 12 9 + 8 24 1 m = 12 17
Solving for m Now, to isolate m , we multiply both sides of the equation by 24: m = 12 17 × 24 We can simplify this by dividing 24 by 12: m = 17 × 2 m = 34
Final Answer Therefore, the solution to the equation is m = 34 .
Examples
Imagine you're baking a cake and need to adjust a recipe. If the original recipe uses 3 2 cup of sugar, but you want to increase the sweetness to 4 3 cup, you need to figure out how much more sugar to add. This problem is similar to solving the equation, where you're finding the unknown amount ( m ) needed to balance the equation. Understanding how to solve such equations helps in real-life scenarios like adjusting recipes, managing budgets, or calculating distances.
After solving the equation 24 1 m − 3 2 = 4 3 , we find that m = 34 . This solution can be obtained by isolating m and manipulating fractions. The correct choice from the options provided is B: m = 34 .
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