What value of $p$ makes the equation true?
$-3 p+\frac{1}{8}=-\frac{1}{4}$
$p=$
Answer (1)
Isolate the term with p by subtracting 8 1 from both sides: − 3 p = − 4 1 − 8 1 .
Simplify the right side by finding a common denominator: − 3 p = − 8 2 − 8 1 = − 8 3 .
Divide both sides by − 3 to solve for p : p = − 3 − 8 3 .
Simplify the expression: p = 8 1 .
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 the 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 − 3 p = − 4 1 − 8 1
Finding a Common Denominator Next, we simplify the right side of the equation by finding a common denominator for the fractions. The common denominator for 4 and 8 is 8. So we rewrite − 4 1 as − 8 2 : − 3 p = − 8 2 − 8 1
Combining Fractions Now, we combine the fractions on the right side: − 3 p = − 8 2 − 8 1 = − 8 3 − 3 p = − 8 3
Solving for p To solve for p , we divide both sides of the equation by − 3 : − 3 − 3 p = − 3 − 8 3 p = − 3 − 8 3
Simplifying the Expression Now, we simplify the expression to find the value of p . Dividing by − 3 is the same as multiplying by − 3 1 : p = − 8 3 × − 3 1 p = 8 3 × 3 1 p = 8 × 3 3 × 1 p = 24 3
Final Simplification Finally, we simplify the fraction: p = 24 3 = 8 1 So, the value of p that makes the equation true is 8 1 .
Examples
This type of problem is useful in balancing chemical equations, where you need to find the right coefficients to make sure the number of atoms is the same on both sides. For example, if you have an equation like 2 x + 2 1 = 1 , solving for x helps you determine the correct amount of a substance needed in a reaction. Similarly, in electrical circuits, you might use such equations to find the value of a resistor needed to achieve a certain voltage or current.
