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What value of $p$ makes the equation true?
[tex]$-3 p+\frac{1}{8}=-\frac{1}{4}$[/tex]
$p=$
Answer (1)
Isolate the term with p by subtracting 8 1 from both sides: − 3 p = − 4 1 − 8 1 .
Combine the fractions on the right side: − 3 p = − 8 3 .
Divide both sides by − 3 to solve for p : p = − 3 − 8 3 .
Simplify the expression to find the value of p : p = 8 1 .
Explanation
Understanding the Problem We are given the equation − 3 p + 8 1 = − 4 1 , and we need to find the value of p that makes this equation true.
Isolating the Term with p First, we want to isolate the term with p . To do this, we subtract 8 1 from both sides of the equation: − 3 p + 8 1 − 8 1 = − 4 1 − 8 1 This simplifies to: − 3 p = − 4 1 − 8 1
Combining Fractions Next, we need to combine the fractions on the right side of the equation. To do this, we need a common denominator, which is 8. So we rewrite − 4 1 as − 8 2 : − 3 p = − 8 2 − 8 1 Now we can combine the fractions: − 3 p = − 8 3
Solving for p Now, we want to solve for p . To do this, we divide both sides of the equation by − 3 : − 3 − 3 p = − 3 − 8 3 This simplifies to: p = − 3 − 8 3
Simplifying the Expression To simplify the expression, we can rewrite the division as multiplication by the reciprocal: p = − 8 3 ⋅ − 3 1 p = 8 3 ⋅ 3 1 Now we can cancel the common factor of 3: p = 8 1
Final Answer Therefore, the value of p that makes the equation true is 8 1 .
Examples
Imagine you're baking a cake and need to adjust a recipe. The recipe calls for a certain amount of flour, but you only want to make a fraction of the cake. Solving linear equations like this helps you determine the exact amount of each ingredient you need to scale the recipe correctly. This is useful not only in cooking but also in various fields like chemistry, where you need to calculate precise amounts of reactants for a chemical reaction, or in finance, where you might need to calculate proportional amounts in investments.
