Oscar tried to solve an equation:
[tex]\begin{aligned}
\frac{3}{4}+m & =\frac{5}{4} \\
\frac{3}{4}+m-\frac{3}{4} & =\frac{5}{4}+\frac{3}{4}
\end{aligned}[/tex]
Answer (2)
The initial equation is 4 3 + m = 4 5 .
Isolate m by subtracting 4 3 from both sides: 4 3 + m − 4 3 = 4 5 − 4 3 .
Simplify the right side: 4 5 − 4 3 = 2 1 .
Therefore, m = 2 1 .
Explanation
Analyzing the Problem Let's analyze Oscar's attempt to solve the equation. The original equation is 4 3 + m = 4 5 . Oscar's next step was to subtract 4 3 from the left side, which is correct. However, he incorrectly added 4 3 to the right side instead of subtracting it. This is where the mistake lies.
Correcting the Equation To isolate m , we need to subtract 4 3 from both sides of the original equation: 4 3 + m = 4 5 4 3 + m − 4 3 = 4 5 − 4 3
Solving for m Now, let's simplify the right side of the equation: 4 5 − 4 3 = 4 5 − 3 = 4 2 = 2 1 So, the correct equation should be: m = 2 1
Identifying the Error Oscar's mistake was adding 4 3 to the right side instead of subtracting it. The correct step should have been:$\frac{3}{4}+m-\frac{3}{4} = \frac{5}{4}-\frac{3}{4},$ which leads to m = 2 1 .
Examples
Imagine you're baking a cake and need to adjust a recipe. If the recipe calls for 4 5 cups of flour, but you've already added 4 3 cups, you need to figure out how much more flour to add. This problem is just like solving the equation 4 3 + m = 4 5 , where m represents the additional amount of flour needed. By subtracting 4 3 from 4 5 , you find that you need to add 2 1 cup more flour. This kind of problem-solving is useful in many real-life situations, from cooking to managing finances.
To solve the equation 4 3 + m = 4 5 , isolate m by subtracting 4 3 from both sides. This leads to m = 2 1 after simplifying the right side. Oscar's mistake was adding 4 3 instead of subtracting it from the right side of the equation.
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